Calculating the perimeter of a quadrilateral - GMAT Quantitative

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Question

Note: Figure NOT drawn to scale

What is the perimeter of Quadrilateral , above?

Answer

By the Pythagorean Theorem,

$\left (AD \right )^{2} +\left ( AU\right ) ^{2} =\left ( DU\right ) ^{2}$

$\left (AD \right )^{2} +4 ^{2} =5 ^{2}$

$\left (AD \right )^{2} +16 =25$

$\left (AD \right )^{2} +16 -16 =25 -16$

$\left (AD \right )^{2} =9$

Also by the Pythagorean Theorem,

$\left ( QU\right ) ^{2} + \left ( DU\right ) ^{2}=\left ( DQ\right ) ^{2}$

$\left ( QU\right ) ^{2} + 5^{2}=13^{2}$

$\left ( QU\right ) ^{2} + 25 =169$

$\left ( QU\right ) ^{2} + 25 -25=169 -25$

$\left ( QU\right ) ^{2} =144$

The perimeter of Quadrilateral is

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Question

What is the perimeter of Rhombus ?

Statement 1:

Statement 2: Rhombus has area .

Answer

A rhombus has four congruent sides. Statement 1 gives the length of one of them, so that length can be multiplied by to yield the perimeter.

The area of a rhombus alone has no bearing on its perimeter, so Statement 2 alone is insufficient.

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Question

Isosceles trapezoid has a side length of . The length of one of its bases (Base A) is equal to three times the amount of seven inches fewer than the length of the other base (Base B). If Base B has a length of , what is the perimeter of ?

Answer

In an isosceles trapezoid, the two non-parallel sides are equal. In this case, they are both long. To find the perimeter, we also need to know the length of both bases. We are told that Base B is . Eliminate any options less than or equal to .

To find the length of Base A, we need to translate the following: "The length of one of its bases (Base A) is equal to three times the amount of seven inches fewer than the length of the other base (Base B)." For translating, break the statement down:

Starting with ,

"seven inches fewer than the length of the other base (Base B)":

"three times the amount of seven inches fewer than the length of the other base (Base B)":

So, Base A is long, so the perimeter of isosceles trapezoid is:

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Question

Frank is planning on fencing a rectangular field near his house. The longer side of the house is two times four more than the length of the other side. If the shorter side is meters, what is the total length of fence that Frank needs?

Answer

This is a perimeter problem, but first we need to find our side lengths.

The short sides are meters. The long sides are two times 4 more than the short sides. So

"four more"

"two times" $60\cdot2=120$ meters

So our two side lengths are 120 and 56 meters. Find the perimeter by the following:

So, 352 meters

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Question

Rhombus has diagonals and . What is the perimeter of the rhombus?

Answer

The rhombus is a special kind of a parallelogram. Its sides are all of the same length. Therefore, we just need to find one length of this quadrilateral. To do so, we can apply the Pythagorean Theorem on triangle AEC for example, since we know the length of the diagonals. Also, the diagonals intersect at their center. Therefore, triangle AEC has length, and . Therefore, $AC=\sqrt{1^{2}+2^{2}}$ or $AC= \sqrt{5}$ . The perimeter is then $4\sqrt{5}$ .

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Question

Note: Figure NOT drawn to scale

What is the perimeter of Quadrilateral , above?

Answer

By the Pythagorean Theorem,

$\left (AD \right )^{2} +\left ( AU\right ) ^{2} =\left ( DU\right ) ^{2}$

$\left (AD \right )^{2} +4 ^{2} =5 ^{2}$

$\left (AD \right )^{2} +16 =25$

$\left (AD \right )^{2} +16 -16 =25 -16$

$\left (AD \right )^{2} =9$

Also by the Pythagorean Theorem,

$\left ( QU\right ) ^{2} + \left ( DU\right ) ^{2}=\left ( DQ\right ) ^{2}$

$\left ( QU\right ) ^{2} + 5^{2}=13^{2}$

$\left ( QU\right ) ^{2} + 25 =169$

$\left ( QU\right ) ^{2} + 25 -25=169 -25$

$\left ( QU\right ) ^{2} =144$

The perimeter of Quadrilateral is

Compare your answer with the correct one above

Question

What is the perimeter of Rhombus ?

Statement 1:

Statement 2: Rhombus has area .

Answer

A rhombus has four congruent sides. Statement 1 gives the length of one of them, so that length can be multiplied by to yield the perimeter.

The area of a rhombus alone has no bearing on its perimeter, so Statement 2 alone is insufficient.

Compare your answer with the correct one above

Question

Isosceles trapezoid has a side length of . The length of one of its bases (Base A) is equal to three times the amount of seven inches fewer than the length of the other base (Base B). If Base B has a length of , what is the perimeter of ?

Answer

In an isosceles trapezoid, the two non-parallel sides are equal. In this case, they are both long. To find the perimeter, we also need to know the length of both bases. We are told that Base B is . Eliminate any options less than or equal to .

To find the length of Base A, we need to translate the following: "The length of one of its bases (Base A) is equal to three times the amount of seven inches fewer than the length of the other base (Base B)." For translating, break the statement down:

Starting with ,

"seven inches fewer than the length of the other base (Base B)":

"three times the amount of seven inches fewer than the length of the other base (Base B)":

So, Base A is long, so the perimeter of isosceles trapezoid is:

Compare your answer with the correct one above

Question

Frank is planning on fencing a rectangular field near his house. The longer side of the house is two times four more than the length of the other side. If the shorter side is meters, what is the total length of fence that Frank needs?

Answer

This is a perimeter problem, but first we need to find our side lengths.

The short sides are meters. The long sides are two times 4 more than the short sides. So

"four more"

"two times" $60\cdot2=120$ meters

So our two side lengths are 120 and 56 meters. Find the perimeter by the following:

So, 352 meters

Compare your answer with the correct one above

Question

Rhombus has diagonals and . What is the perimeter of the rhombus?

Answer

The rhombus is a special kind of a parallelogram. Its sides are all of the same length. Therefore, we just need to find one length of this quadrilateral. To do so, we can apply the Pythagorean Theorem on triangle AEC for example, since we know the length of the diagonals. Also, the diagonals intersect at their center. Therefore, triangle AEC has length, and . Therefore, $AC=\sqrt{1^{2}+2^{2}}$ or $AC= \sqrt{5}$ . The perimeter is then $4\sqrt{5}$ .

Compare your answer with the correct one above

Question

Note: Figure NOT drawn to scale

What is the perimeter of Quadrilateral , above?

Answer

By the Pythagorean Theorem,

$\left (AD \right )^{2} +\left ( AU\right ) ^{2} =\left ( DU\right ) ^{2}$

$\left (AD \right )^{2} +4 ^{2} =5 ^{2}$

$\left (AD \right )^{2} +16 =25$

$\left (AD \right )^{2} +16 -16 =25 -16$

$\left (AD \right )^{2} =9$

Also by the Pythagorean Theorem,

$\left ( QU\right ) ^{2} + \left ( DU\right ) ^{2}=\left ( DQ\right ) ^{2}$

$\left ( QU\right ) ^{2} + 5^{2}=13^{2}$

$\left ( QU\right ) ^{2} + 25 =169$

$\left ( QU\right ) ^{2} + 25 -25=169 -25$

$\left ( QU\right ) ^{2} =144$

The perimeter of Quadrilateral is

Compare your answer with the correct one above

Question

What is the perimeter of Rhombus ?

Statement 1:

Statement 2: Rhombus has area .

Answer

A rhombus has four congruent sides. Statement 1 gives the length of one of them, so that length can be multiplied by to yield the perimeter.

The area of a rhombus alone has no bearing on its perimeter, so Statement 2 alone is insufficient.

Compare your answer with the correct one above

Question

Isosceles trapezoid has a side length of . The length of one of its bases (Base A) is equal to three times the amount of seven inches fewer than the length of the other base (Base B). If Base B has a length of , what is the perimeter of ?

Answer

In an isosceles trapezoid, the two non-parallel sides are equal. In this case, they are both long. To find the perimeter, we also need to know the length of both bases. We are told that Base B is . Eliminate any options less than or equal to .

To find the length of Base A, we need to translate the following: "The length of one of its bases (Base A) is equal to three times the amount of seven inches fewer than the length of the other base (Base B)." For translating, break the statement down:

Starting with ,

"seven inches fewer than the length of the other base (Base B)":

"three times the amount of seven inches fewer than the length of the other base (Base B)":

So, Base A is long, so the perimeter of isosceles trapezoid is:

Compare your answer with the correct one above

Question

Frank is planning on fencing a rectangular field near his house. The longer side of the house is two times four more than the length of the other side. If the shorter side is meters, what is the total length of fence that Frank needs?

Answer

This is a perimeter problem, but first we need to find our side lengths.

The short sides are meters. The long sides are two times 4 more than the short sides. So

"four more"

"two times" $60\cdot2=120$ meters

So our two side lengths are 120 and 56 meters. Find the perimeter by the following:

So, 352 meters

Compare your answer with the correct one above

Question

Rhombus has diagonals and . What is the perimeter of the rhombus?

Answer

The rhombus is a special kind of a parallelogram. Its sides are all of the same length. Therefore, we just need to find one length of this quadrilateral. To do so, we can apply the Pythagorean Theorem on triangle AEC for example, since we know the length of the diagonals. Also, the diagonals intersect at their center. Therefore, triangle AEC has length, and . Therefore, $AC=\sqrt{1^{2}+2^{2}}$ or $AC= \sqrt{5}$ . The perimeter is then $4\sqrt{5}$ .

Compare your answer with the correct one above

Question

Note: Figure NOT drawn to scale

What is the perimeter of Quadrilateral , above?

Answer

By the Pythagorean Theorem,

$\left (AD \right )^{2} +\left ( AU\right ) ^{2} =\left ( DU\right ) ^{2}$

$\left (AD \right )^{2} +4 ^{2} =5 ^{2}$

$\left (AD \right )^{2} +16 =25$

$\left (AD \right )^{2} +16 -16 =25 -16$

$\left (AD \right )^{2} =9$

Also by the Pythagorean Theorem,

$\left ( QU\right ) ^{2} + \left ( DU\right ) ^{2}=\left ( DQ\right ) ^{2}$

$\left ( QU\right ) ^{2} + 5^{2}=13^{2}$

$\left ( QU\right ) ^{2} + 25 =169$

$\left ( QU\right ) ^{2} + 25 -25=169 -25$

$\left ( QU\right ) ^{2} =144$

The perimeter of Quadrilateral is

Compare your answer with the correct one above

Question

What is the perimeter of Rhombus ?

Statement 1:

Statement 2: Rhombus has area .

Answer

A rhombus has four congruent sides. Statement 1 gives the length of one of them, so that length can be multiplied by to yield the perimeter.

The area of a rhombus alone has no bearing on its perimeter, so Statement 2 alone is insufficient.

Compare your answer with the correct one above

Question

Isosceles trapezoid has a side length of . The length of one of its bases (Base A) is equal to three times the amount of seven inches fewer than the length of the other base (Base B). If Base B has a length of , what is the perimeter of ?

Answer

In an isosceles trapezoid, the two non-parallel sides are equal. In this case, they are both long. To find the perimeter, we also need to know the length of both bases. We are told that Base B is . Eliminate any options less than or equal to .

To find the length of Base A, we need to translate the following: "The length of one of its bases (Base A) is equal to three times the amount of seven inches fewer than the length of the other base (Base B)." For translating, break the statement down:

Starting with ,

"seven inches fewer than the length of the other base (Base B)":

"three times the amount of seven inches fewer than the length of the other base (Base B)":

So, Base A is long, so the perimeter of isosceles trapezoid is:

Compare your answer with the correct one above

Question

Frank is planning on fencing a rectangular field near his house. The longer side of the house is two times four more than the length of the other side. If the shorter side is meters, what is the total length of fence that Frank needs?

Answer

This is a perimeter problem, but first we need to find our side lengths.

The short sides are meters. The long sides are two times 4 more than the short sides. So

"four more"

"two times" $60\cdot2=120$ meters

So our two side lengths are 120 and 56 meters. Find the perimeter by the following:

So, 352 meters

Compare your answer with the correct one above

Question

Rhombus has diagonals and . What is the perimeter of the rhombus?

Answer

The rhombus is a special kind of a parallelogram. Its sides are all of the same length. Therefore, we just need to find one length of this quadrilateral. To do so, we can apply the Pythagorean Theorem on triangle AEC for example, since we know the length of the diagonals. Also, the diagonals intersect at their center. Therefore, triangle AEC has length, and . Therefore, $AC=\sqrt{1^{2}+2^{2}}$ or $AC= \sqrt{5}$ . The perimeter is then $4\sqrt{5}$ .

Compare your answer with the correct one above

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