Calculating the length of the hypotenuse of a right triangle : Pythagorean Theorem - GMAT Quantitative

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Question

What is the hypotenuse of a right triangle with sides 14 and 48?

Answer

For starters, we know that the hypotenuse is the longest side of a triangle, so we can immediately cross off 25 as an answer choice because it is smaller than one of the legs, 48. To find the hypotenuse, we can use the Pythagorean Theorem.

$hypotenuse^{^{2}} = 14^{2} + 48^{2} = 2500$

$hypotenuse = 50$

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Question

What is the length of a right triangle hypotenuse if the the other two sides are and units long?

Answer

To find a length of a side in a right triangle, we can use the Pythagorean theorem:

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Question

A right triangle has a height of 8 and a base of 15. What is the length of its hypotenuse?

Answer

We are given the length of the height and the base, so we can use the Pythagorean theorem to calculate the length of the hypotenuse:

$c^2=289\rightarrow c=\sqrt{289}=17$

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Question

What is the hypotenuse of a right triangle with legs of lengths and ?

Answer

In order to find the value of the hypotenuse , we need to plug the values of the legs and into the Pythagorean Theorem: $a^{2}+b^{2}=c^{2}$

$(7cm)^{2}+(9cm)^{2}=c^{2}$

$49cm+81cm=c^{2}$

$130cm=c^{2}$

$\sqrt{130}cm=c$

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Question

What is the hypotenuse of a right triangle with legs of length and ?

Answer

In order to find the value of the hypotenuse , we need to plug the values of the legs and into the Pythagorean Theorem: $a^{2}+b^{2}=c^{2}$

$5^{2}+7^{2}=c^{2}$

$25+49=c^{2}$

$74=c^{2}$

$\sqrt{74}=c$

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Question

What is the hypotenuse of a right triangle with an area of and a leg length of ?

Answer

In order to find the value of the hypotenuse given area and leg length , we first need to calculate the length of the other leg length . Given the area equation $A=\frac{1}{2}ab$ :

$\frac{2A}{b}=a$

Plugging in and :

$\frac{2(30)}{12}=a$

$\frac{60}{12}=a$

Now we need to plug the values of the legs and into the Pythagorean Theorem: $a^{2}+b^{2}=c^{2}$

$5^{2}+12^{2}=c^{2}$

$25+144=c^{2}$

$25+144=c^{2}$

$169=c^{2}$

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Question

Each leg of a $\textup{45-45-90}$ triangle has length $2 ^{K}$ . Give the length of its hypotenuse.

Answer

The hypotenuse of a $\textup{45-45-90}$ triangle has length $\sqrt{2} = 2^{\frac{1}{2}}$ times that of a leg, which here is

$2 ^{K} \cdot 2^{\frac{1}{2}} = 2 ^{K+ \frac{1}{2}}$ .

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Question

What is the hypotenuse of a right triangle with sides 14 and 48?

Answer

For starters, we know that the hypotenuse is the longest side of a triangle, so we can immediately cross off 25 as an answer choice because it is smaller than one of the legs, 48. To find the hypotenuse, we can use the Pythagorean Theorem.

$hypotenuse^{^{2}} = 14^{2} + 48^{2} = 2500$

$hypotenuse = 50$

Compare your answer with the correct one above

Question

What is the length of a right triangle hypotenuse if the the other two sides are and units long?

Answer

To find a length of a side in a right triangle, we can use the Pythagorean theorem:

Compare your answer with the correct one above

Question

A right triangle has a height of 8 and a base of 15. What is the length of its hypotenuse?

Answer

We are given the length of the height and the base, so we can use the Pythagorean theorem to calculate the length of the hypotenuse:

$c^2=289\rightarrow c=\sqrt{289}=17$

Compare your answer with the correct one above

Question

What is the hypotenuse of a right triangle with legs of lengths and ?

Answer

In order to find the value of the hypotenuse , we need to plug the values of the legs and into the Pythagorean Theorem: $a^{2}+b^{2}=c^{2}$

$(7cm)^{2}+(9cm)^{2}=c^{2}$

$49cm+81cm=c^{2}$

$130cm=c^{2}$

$\sqrt{130}cm=c$

Compare your answer with the correct one above

Question

What is the hypotenuse of a right triangle with legs of length and ?

Answer

In order to find the value of the hypotenuse , we need to plug the values of the legs and into the Pythagorean Theorem: $a^{2}+b^{2}=c^{2}$

$5^{2}+7^{2}=c^{2}$

$25+49=c^{2}$

$74=c^{2}$

$\sqrt{74}=c$

Compare your answer with the correct one above

Question

What is the hypotenuse of a right triangle with an area of and a leg length of ?

Answer

In order to find the value of the hypotenuse given area and leg length , we first need to calculate the length of the other leg length . Given the area equation $A=\frac{1}{2}ab$ :

$\frac{2A}{b}=a$

Plugging in and :

$\frac{2(30)}{12}=a$

$\frac{60}{12}=a$

Now we need to plug the values of the legs and into the Pythagorean Theorem: $a^{2}+b^{2}=c^{2}$

$5^{2}+12^{2}=c^{2}$

$25+144=c^{2}$

$25+144=c^{2}$

$169=c^{2}$

Compare your answer with the correct one above

Question

Each leg of a $\textup{45-45-90}$ triangle has length $2 ^{K}$ . Give the length of its hypotenuse.

Answer

The hypotenuse of a $\textup{45-45-90}$ triangle has length $\sqrt{2} = 2^{\frac{1}{2}}$ times that of a leg, which here is

$2 ^{K} \cdot 2^{\frac{1}{2}} = 2 ^{K+ \frac{1}{2}}$ .

Compare your answer with the correct one above

Question

What is the hypotenuse of a right triangle with sides 14 and 48?

Answer

For starters, we know that the hypotenuse is the longest side of a triangle, so we can immediately cross off 25 as an answer choice because it is smaller than one of the legs, 48. To find the hypotenuse, we can use the Pythagorean Theorem.

$hypotenuse^{^{2}} = 14^{2} + 48^{2} = 2500$

$hypotenuse = 50$

Compare your answer with the correct one above

Question

What is the length of a right triangle hypotenuse if the the other two sides are and units long?

Answer

To find a length of a side in a right triangle, we can use the Pythagorean theorem:

Compare your answer with the correct one above

Question

A right triangle has a height of 8 and a base of 15. What is the length of its hypotenuse?

Answer

We are given the length of the height and the base, so we can use the Pythagorean theorem to calculate the length of the hypotenuse:

$c^2=289\rightarrow c=\sqrt{289}=17$

Compare your answer with the correct one above

Question

What is the hypotenuse of a right triangle with legs of lengths and ?

Answer

In order to find the value of the hypotenuse , we need to plug the values of the legs and into the Pythagorean Theorem: $a^{2}+b^{2}=c^{2}$

$(7cm)^{2}+(9cm)^{2}=c^{2}$

$49cm+81cm=c^{2}$

$130cm=c^{2}$

$\sqrt{130}cm=c$

Compare your answer with the correct one above

Question

What is the hypotenuse of a right triangle with legs of length and ?

Answer

In order to find the value of the hypotenuse , we need to plug the values of the legs and into the Pythagorean Theorem: $a^{2}+b^{2}=c^{2}$

$5^{2}+7^{2}=c^{2}$

$25+49=c^{2}$

$74=c^{2}$

$\sqrt{74}=c$

Compare your answer with the correct one above

Question

What is the hypotenuse of a right triangle with an area of and a leg length of ?

Answer

In order to find the value of the hypotenuse given area and leg length , we first need to calculate the length of the other leg length . Given the area equation $A=\frac{1}{2}ab$ :

$\frac{2A}{b}=a$

Plugging in and :

$\frac{2(30)}{12}=a$

$\frac{60}{12}=a$

Now we need to plug the values of the legs and into the Pythagorean Theorem: $a^{2}+b^{2}=c^{2}$

$5^{2}+12^{2}=c^{2}$

$25+144=c^{2}$

$25+144=c^{2}$

$169=c^{2}$

Compare your answer with the correct one above

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