Question

A square and a rectangle have the same area. The length of the rectangle is 3 inches more than the side of the square. The width of the rectangle is two inches less than the side of the square. Algebraically, find the side of the square.

Plzzzzzz help

Answer 1

6 inches

Explanation:

Let s represent the length of the side of the square in inches. Then the rectangle dimensions are ...

length: s + 3

width: s - 2

The area of the rectangle is the product of these, so is ...

(s +3)(s -2) = s² +s -6

This is the same as the area of the square, which is s², so we have ...

s² = s² +s -6 . . . . square area = rectangle area

0 = s - 6 . . . . . . . subtract s²

6 = s . . . . . . . . . . add 6

The side of the square is 6 inches.

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Check

The area of the square is 6² = 36.

The area of the rectangle is 9×4 = 36. (answer meets problem conditions)