Question

the dimensions of a square are altered so that one dimension is increased by 7 feet and the other is decreased by 2 feet. The area of the resulting rectangle is 90 sq. feet. find the original area of the square

Answer 1

The original area of the square was 24

Explanation:

Let's say the dimension of the new square is 9 and 10, that'll make 90

Let's say the original dimensions were 9 - 7, 10 + 2 which is 2, 12

The area of the original dimensions is 24 square feet and they altered that to make the resulting rectangle 90 square feet.

Answer 2

The area of the original SQUARE is 64 sq feet. x = 8

It was an 8 × 8 SQUARE.

Explanation:

Let x = the original side length.

x + 7 is a new side

x - 2 is the other new side. Its a rectangle now.

Area of a rectangle:

A = length × width

A = (x+7)(x-2)

90 = x^2 +5x -14

Solve. Subtract 90.

0 = x^2 + 5x - 104

Factor.

0 = (x + 13)(x - 8)

x + 13 = 0 and x-8=0

x = -13 and x = 8

-13 is discarded because lengths cannot be negative.

x = 8 is the original side length of the square.

Area is 8×8 = 64 sqft