How to find the perimeter of a rectangle - SSAT Middle Level Quantitative

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Question

What is the perimeter of a rectangle with a width of 3 and a length of 10?

Answer

The formula for the perimeter of a rectangle is $\dpi{100} Perimeter=2l+2w$ .

Plug in our given values to solve:

$\dpi{100} Perimeter = 2(20)+2(3)$

$\dpi{100} Perimeter = 20+6$

$\dpi{100} Perimeter = 26$

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Question

Rectangle ABCD has an area of . If the width of the rectangle is , what is the perimeter?

Answer

The area of a rectangle is found by multiplying the length times the width. The question tells you the width is and the area is .

Thus the length is 8. $\left ( 40 \div5\right)$ .

To find the perimeter you add up all of the sides.

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Question

The width of a rectangle is half of its length. If the width is given as __what is the perimeter of the rectangle in terms of ?

Answer

The sum of the widths is __and since the width is half the length, each length is . Since there are 2 lengths we get a total perimeter of .

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Question

How many meters of fence are needed to enclose a rectangular field that has a length of 1000 meters and a width of 100 meters?

Answer

The perimeter of a rectangle is simply the sum of the four sides:

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Question

The above figure shows the size and shape of a yard that is to be surrounded by some fence. How many feet of fence will be needed?

Note: all sides meet at right angles.

Answer

The best way to see that 750 feet of fence are needed is to look at this augmented diagram.

Note that two of the sides are extended to form a smaller rectangle whose sides can be deduced by subtraction. Since opposite sides of a rectangle are congruent, this allows us to fill in the two missing sidelengths of the original figure.

Now add: $150+110+70+115+80+225 = 750 \textrm{ft}$

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Question

Give the perimeter of the rectangle in the above diagram.

Answer

The perimeter of a rectangle is the sum of the length and the width, multiplied by 2:

$2 (12.6 + 6.4) = 2 \cdot 19 = 38$

The rectangle has a perimeter of 38 centimeters.

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Question

Give the perimeter of the rectangle in the above diagram.

Answer

The perimeter of a rectangle can be calculated by multiplying two by the sum of the length and width of the rectangle.

$2\left ( 7 \frac{1}{2} +5 \frac{3}{5} \right )$

$=2 \left (\frac{7 \cdot 2 + 1}{2} + \frac{5\cdot 5 + 3}{5} \right )$

$= 2 \left (\frac{15}{2} + \frac{28}{5} \right )$

$= 2 \left (\frac{15 \times 5}{2 \times 5} + \frac{2 \times28}{2 \times5} \right )$

$= 2 \left (\frac{75}{10} + \frac{56}{10} \right ) = \frac{2}{1} \cdot \frac{131}{10} = \frac{131}{5} = 26 \frac{1}{5}$

The perimeter of the rectangle is $26 \frac{1}{5}$ inches.

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Question

Give the perimeter of the above rectangle in centimeters, using the conversion factor centimeters per yard.

Answer

The perimeter of the rectangle is yards. To convert this to centimeters, multiply by the given conversion factor:

$91.44 \times 22 = 2,011.68$ centimeters.

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Question

A rectangle has an area of . The length of each side is a whole number. What is NOT a possible value for the rectangle's perimeter?

Answer

Since each side is a whole number, first find the whole number factors of . They are and , and , and , and and . These sidelengths correspond to perimeters of , , , and , respectively. Thus, is answer.

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Question

You are given equilateral triangle $\Delta ABC$ and Rectangle

with .

What is the perimeter of Rectangle ?

Answer

$\Delta ABC$ is equilateral, so .

Also, since opposite sides of a rectangle are congruent,

and

The perimeter of Rectangle is

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Question

The length of a rectangle is two times as long as the width. The width is equal to inches. What is the perimeter of the rectangle?

Answer

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Question

A hectare is a unit of area equal to 10,000 square meters.

A 150-hectare plot of land is rectangular and is 1.2 kilometers in width. Give the perimeter of this land.

Answer

150 hectares is equal to $150 \times 10,000 = 1,500,000$ square meters.

The width of this land is 1.2 kilometers, or $1.2 \times 1,000 =1,200$ meters. Divide the area by the width to get:

$1,500,000 \div 1,200 = 1,250$ meters

The perimeter of the land is

$2 \left ( 1,200 + 1,250\right ) = 4,900$ meters, or $4,900 \div 1,000 = 4.9$ kilometers.

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Question

The perimeter of a rectangle with a length of and a width of is $64\ in$ . Find .

Answer

We know that:

where:

$a=Length \ of\ the\ rectangle$

$b= Width\ of\ the\ rectangle$

So we can write:

$64=2(10x+6x)\Rightarrow 10x+6x=32\Rightarrow 16x=32\Rightarrow x=2$

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Question

The width of a rectangle is , the length is , and the perimeter is 72. What is the value of ?

Answer

Start with the equation for the perimeter of a rectangle:

We know the perimeter is 72, the length is , and the width is . Plug these values into our equation.

Multiply and combine like terms.

Divide by 18 to isolate the variable.

$\frac{72}{18}=x$

Simplify the fraction by removing the common factor.

$\frac{72}{18}=\frac{72\div18}{18\div18}=\frac{4}{1}=4$

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Question

If the perimeter of a rectangle is inches and the width is inches, what is the length?

Answer

The perimeter of a rectangle is represented by the following formula, in which W represents width and L represents length:

Given that the width is inches and that the perimeter is inches, the following applies:

$2\cdot 2+2L=14$

Next, subtract from each side.

Now, divide each side by .

This gives us

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Question

Note: Figure NOT drawn to scale.

Refer to the above diagram. Give the perimeter of the red polygon.

Answer

Since opposite sides of a rectangle have the same measure, the missing sidelengths can be calculated as in the diagram below:

The sidelengths of the red polygon can now be added to find the perimeter:

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Question

Note: Figure NOT drawn to scale.

Refer to the above diagram. Give the ratio of the perimeter of the large rectangle to that of the smaller rectangle.

Answer

Opposite sides of a rectangle are congruent.

The large rectangle has perimeter

.

The smaller rectangle has perimeter

.

The ratio is

$\frac{240}{100} = \frac{240 \div 20 }{100\div 20 } = \frac{12}{5}$ ; that is, 12 to 5.

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Question

Figure NOT drawn to scale.

Give the perimeter of the green polygon in the above figure.

Answer

Since opposite sides of a rectangle have the same measure, the missing sidelengths can be calculated as in the diagram below:

The sidelengths of the green polygon can now be added to find the perimeter:

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Question

The width of a rectangle is one-third of its length. If the width is given as what is the perimeter of the rectangle in terms of ?

Answer

The perimeter of a rectangle is the sum of its sides.

The sum of the widths is and since the width is one-third of the length, each length is . Since there are lengths we get a total of . Widths + lengths =

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Question

Find the perimeter of the rectangle shown below

Answer

The perimeter of a rectangle, or any shape, is the distance around the outside. You add up the length of each side to find this number. The coordinates of the points are . You need to find the distance between each point. The short side is units, and the longer side is units.

$(8\times2)+(10\times2)=16+20=36$

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