### All ISEE Middle Level Math Resources

## Example Questions

### Example Question #51 : Rectangles

You are given equilateral triangle and Rectangle

with .

What is the perimeter of Rectangle ?

**Possible Answers:**

**Correct answer:**

is equilateral, so .

Also, since opposite sides of a rectangle are congruent,

and

The perimeter of Rectangle is

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

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

**Correct answer:**

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

**Possible Answers:**

**Correct answer:**

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

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

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

**Possible Answers:**

**Correct answer:**

We know that:

where:

So we can write:

### Example Question #11 : How To Find The Perimeter Of A Rectangle

Note: Figure NOT drawn to scale.

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

**Possible Answers:**

The perimeter cannot be determined from the information given.

**Correct 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:

### Example Question #11 : Rectangles

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

**Possible Answers:**

**Correct 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.

Simplify the fraction by removing the common factor.

### Example Question #222 : Plane Geometry

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.

**Possible Answers:**

The correct answer is not given among the other choices.

**Correct answer:**

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 #11 : How To Find The Perimeter Of A Rectangle

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

**Possible Answers:**

26

60

30

13

12

**Correct answer:**

26

The formula for the perimeter of a rectangle is .

Plug in our given values to solve:

### Example Question #122 : Geometry

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

**Possible Answers:**

**Correct 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:

Next, subtract from each side.

Now, divide each side by .

This gives us

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