# ISEE Middle Level Quantitative : Geometry

## Example Questions

### Example Question #1 : How To Find Perimeter

If a square has sides measuring , what is the perimeter of the square, in simplest form?

Possible Answers:

Correct answer:

Explanation:

To find the perimeter of a square, you must add together all the sides. In this case, we are adding four times.

Since all of the denominators are the same, there is no need to find a commond denominator, so we add together the numerators.  This gives us .

Since both the numerator and denomator are divisible by four, we must simplify this fraction.

The perimeter of the square is .

### Example Question #1 : How To Find Perimeter

The sum of the lengths of three sides of a square is one foot. Give the perimeter of the square in inches.

Possible Answers:

It is impossible to determine the perimeter from the information given.

Correct answer:

Explanation:

A square has four sides of the same length.

One foot is equal to twelve inches; since the sum of the lengths of three of the congruent sides is twelve inches, each side measures

inches.

The perimeter is

inches.

### Example Question #1 : How To Find Perimeter

A square has perimeter one yard. Which is the greater quantity?

(A) The length of one side of the square

(B) 8 inches

Possible Answers:

It is impossible to determine which is greater from the information given

(A) and (B) are equal

(A) is greater

(B) is greater

Correct answer:

(A) is greater

Explanation:

One yard is equal to 36 inches. A square has four sides of equal length, so one side of the square has length

inches.

Since , (A) is greater.

### Example Question #2 : How To Find Perimeter

A square has perimeter five meters. Which is the greater quantity?

(A) 1,250 millimeters

(B) The length of one side of the square

Possible Answers:

(A) is greater

(B) is greater

(A) and (B) are equal

It is impossible to determine which is greater from the information given

Correct answer:

(A) and (B) are equal

Explanation:

One meter is equal to 1,000 millimeters, so the square has perimeter

millimeters.

A square has four sides of equal length, so one side of the square has length

millimeters.

The quantities are equal.

### Example Question #1 : How To Find Perimeter

A square lot has perimeter one mile. Which is the greater quantity?

(A) 1,320 feet

(B) The length of one side of the square

Possible Answers:

(A) and (B) are equal

(A) is greater

It is impossible to tell which is greater from the information given

(B) is greater

Correct answer:

(A) and (B) are equal

Explanation:

One mile is equal to 5,280 feet. A square has four sides of equal length, so one side of the square has length

feet.

The quantities are equal.

### Example Question #11 : Plane Geometry

The sum of the lengths of three sides of a square is 9,000 centimeters. Give its perimeter in meters.

Possible Answers:

Correct answer:

Explanation:

100 centimeters are equal to one meter, so 9,000 centimeters are equal to

meters.

A square has four sides of the same length. Since the sum of the lengths of three of the congruent sides is 9,000 centimeters, or 90 meters, each side measures

meters.

The perimeter is four times this, which is

meters.

### Example Question #6 : How To Find Perimeter

A square has perimeter one meter. Which is the greater quantity?

(A) 250 centimeters

(B) The length of one side of the square

Possible Answers:

(B) is greater

It is impossible to tell which is greater from the information given

(A) is greater

(A) and (B) are equal

Correct answer:

(A) is greater

Explanation:

One meter is equal to 100 centimeters.

A square has four sides of equal length, so we will need to divide by 4 to find the length of one side.

, so (A) is greater

### Example Question #7 : How To Find Perimeter

Each side of a square is  units long. Which is the greater quantity?

(A)

(B) The perimeter of the square

Possible Answers:

(A) and (B) are equal

(A) is greater

It is impossible to determine which is greater from the information given

(B) is greater

Correct answer:

(A) and (B) are equal

Explanation:

The perimeter of a square is four times its side length:

Since the perimeter is equal to , (A) and (B) are equal.

### Example Question #1 : How To Find Perimeter

Hexagon  and Square  both have perimeter 64. Which is the greater quantity?

(a)

(b)

Possible Answers:

(a) is the greater quantity

It is impossible to determine which is greater from the information given

(b) is the greater quantity

(a) and (b) are equal

Correct answer:

It is impossible to determine which is greater from the information given

Explanation:

The length of one side of the square - in particular, that of  - is equal to one fourth its perimeter, so it can be determined that . However, no relation among the sides of the hexagon is given - in particular, it is not given that the hexagon is regular - so the length of  cannot be determined. Insufficient information is given.

### Example Question #22 : How To Find The Area Of A Parallelogram

What is the length of a rectangular room with a perimeter of  and a width of

Possible Answers:

Correct answer:

Explanation:

We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown.

Subtract  from both sides

Divide  by both sides