How to find the length of the side of a square - ISEE Upper Level (grades 9-12) Quantitative Reasoning

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Question

Which is the greater quantity?

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

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

Answer

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.

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Question

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.

Answer

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.

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Question

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

Answer

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

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