### All ISEE Upper Level Quantitative Resources

## Example Questions

### Example Question #231 : Plane Geometry

Which is the greater quantity?

(a) The sidelength of a square with area 400 square inches.

(b) The sidelength of a square with perimeter 80 inches.

**Possible Answers:**

(a) is greater

(b) is greater

(a) and (b) are equal

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

**Correct answer:**

(a) and (b) are equal

The sidelength of a square is the square root of its area and one-fourth of its perimeter, so:

(a) A square with area 400 square inches has sidelength inches.

(b) A square with perimeter 80 inches has sidelength inches.

The two quantities are equal.

### Example Question #2 : How To Find The Length Of The Side Of A Square

Which is the greater quantity?

(a) The sidelength of a square with area square inches.

(b) The sidelength of a square with perimeter inches.

**Possible Answers:**

(a) is greater.

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

(a) and (b) are equal.

(b) is greater.

**Correct answer:**

(a) is greater.

The sidelength of a square is the square root of its area and one-fourth of its perimeter, so:

(a) A square with area square inches has sidelength inches.

(b) A square with perimeter inches has sidelength inches.

(a) is the greater quantity.

### Example Question #3 : How To Find The Length Of The Side Of A Square

The perimeter of a square is . Give the length of each side in terms of .

**Possible Answers:**

**Correct answer:**

Divide the perimeter of a square by 4 to get its sidelength: