How to find the perimeter of the rectangle - ISEE Middle Level Quantitative Reasoning

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Question

The Smartboard in your math classroom is 3 feet tall and 20 feet long. What is the perimeter of the Smartboard?

Answer

The Smartboard in your math classroom is 3 feet tall and 20 feet long. What is the perimeter of the Smartboard?

We need to find the perimeter of the rectangle that is the Smartboard.

To do so, we simply add up the sides. In this case, we have 2 3ft sides and 2 20 ft sides.

So our answer is 46

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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

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

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

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

Find the distance around a rug if the rug is 2 feet wide and its length is 3 times the width.

Answer

Find the distance around a rectangular rug if the rug is 2 feet wide and its length is 3 times the width.

We are really being asked to find the perimeter. To do so, we first need to dimensions.

We are told the width is two feet.

The length is three times the width.

Now, use the following to find the perimeter:

$p_{rectangle}=2l+2w=2(6ft)+2(2ft)=12ft+4ft=16ft$

So our answer is 16 feet

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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

Find the perimeter of a rectangle whose length is 6 and width is 5.

Answer

To solve, simply use the formula for the perimeter of a rectangle.

In this particular case the length and width are,

Thus,

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Question

A rectangle has a length of 9 centimeters and a width of 5 centimeters. Find the perimeter.

Answer

The formula for the perimeter of a rectangle is:

where

$P = 2 \times 14$

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Question

The length of a rectangle is 1 cm more than 3 times the width. What is the perimeter of the rectangle if the width is 32 cm?

Answer

First find the length.

length or

$(3 \times 32) + 1 = 97$

The length is

Find the perimeter.

The perimeter is when the width is .

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Question

Use the following to answer the question.

Find the perimeter of the rectangle if the width is half the length.

Answer

To find the perimeter of a rectangle, we use the following formula:

$\text{perimeter of rectangle} = a+b+c+d$

where a, b, c, and _d_are the lengths of the sides of the rectangle.

Now, in the rectangle

we can see the length is 12 feet. Because it is a rectangle, we know the opposite side is also 12 feet. We know the width is half of the length. So, the width is 6 feet. Because it is a rectangle, the opposite side is also 6 feet. Knowing this, we can substitute into the formula. We get

$\text{perimeter of rectangle} = 12\text{ft} + 12\text{ft} + 6\text{ft} + 6\text{ft}$

$\text{perimeter of rectangle} = 36\text{ft}$

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Question

Refer to the above figures. The square at left has perimeter 160. Give the perimeter of the rectangle at right.

Answer

The perimeter of a square is four times the length of a side - here, this is .

The perimeter of a rectangle is twice the sum of its length and its width - here, this is $2 \left ( \frac{1}{2} x + 2x \right ) = 2 \left ( 2\frac{1}{2} x \right ) = 5x$ .

The square has perimeter 160, so

$4x \div 4 = 160 \div 4$

The perimeter of the rectangle is .

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Question

A rectangular postage stamp has a width of 3 cm and a height of 12 cm. Find the perimeter of the stamp.

Answer

A rectangular postage stamp has a width of 3 cm and a height of 12 cm. Find the perimeter of the stamp.

To find the perimeter of a rectangle (or any shape) simply add up all the sides.

In this case, we have two sides that are 3 cm and two sides that are 12 cm.

Now, our answer must be in centimeters and not centimeters squared, because we are dealing with perimeter, which is a measure of length.

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Question

Find the perimeter of a rectangle with a width of 6 cm and a length that is two times the width.

Answer

To find the perimeter of a rectangle, we will use the following formula:

$\text{perimeter of rectangle} = a+b+c+d$

where a, b, c, and d are the lengths of the sides of the rectangle.

Now, we know the width of the rectangle is 6cm. Because it is a rectangle, we know the opposite side is equal. Therefore, the opposite side is also 6cm.

We also know the length is two times the width. Therefore, the length is 12cm. Because it is a rectangle, we know the opposite side is equal. Therefore, the opposite side is also 12cm.

Knowing this, we can substitute into the formula. We get

$\text{perimeter of rectangle} = 6\text{cm} + 6\text{cm} + 12\text{cm} + 12\text{cm}$

$\text{perimeter of rectangle} = 36\text{cm}$

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