# ISEE Middle Level Math : How to find the perimeter of the rectangle

## Example Questions

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### Example Question #7 : How To Find The Perimeter Of A Rectangle

You are given equilateral triangle  and Rectangle

with .

What is the perimeter of Rectangle  ?

Explanation:

is equilateral, so .

Also, since opposite sides of a rectangle are congruent,

and

The perimeter of Rectangle  is

### Example Question #8 : How To Find The Perimeter Of A Rectangle

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.

Explanation:

150 hectares is equal to  square meters.

The width of this land is 1.2 kilometers, or  meters. Divide the area by the width to get:

meters

The perimeter of the land is

meters, or  kilometers.

### Example Question #1 : How To Find The Perimeter Of A Rectangle

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?

Explanation:

### Example Question #1 : How To Find The Perimeter Of A Rectangle

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?

Explanation:

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

### Example Question #11 : Rectangles

The perimeter of a rectangle with a length of  and a width of is . Find .

Explanation:

We know that:

where:

So we can write:

### Example Question #12 : Rectangles

Note: Figure NOT drawn to scale.

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

The perimeter cannot be determined from the information given.

Explanation:

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:

### Example Question #13 : Rectangles

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

Explanation:

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.

Simplify the fraction by removing the common factor.

### Example Question #121 : Quadrilaterals

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.

The correct answer is not given among the other choices.

Explanation:

Opposite sides of a rectangle are congruent.

The large rectangle has perimeter

.

The smaller rectangle has perimeter

.

The ratio is

; that is, 12 to 5.

### Example Question #1 : How To Find The Perimeter Of The Rectangle

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

26

30

12

13

60

26

Explanation:

The formula for the perimeter of a rectangle is .

Plug in our given values to solve:

### Example Question #17 : Rectangles

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

Explanation:

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:

Next, subtract  from each side.

Now, divide each side by .

This gives us

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