How long is a side of the original square banner?

Question

A square banner had 4 feet added its width and 2 feet subtracted from its height. The banner then had an area of 91 square feet. How long was a side of the original square banner?

Answer 1

A square banner (call sides x)

...had 4 feet added its width

x + 4

...and 2 feet subtracted from its height.

x - 2

The banner then had an area of 91 square feet.

(x+4)(x -2) = 91

x^2 +2x - 8 = 91

x^2 + 2x -99 = 0

factorise

(x + 11)(x - 9) = 0

x = - 11 (reject negative value)

x = 9 feet

Answer 2

91 = 7 * 13 (prime factors)

The side was originally 7+2 = 13-4 = 9 feet long.

Answer 3

x = original side length in ft

(x+4)(x-2) = 91

x^2+2x-99 = 0

(x+11)(x-9) = 0]

x = 9 ft

Answer 4

(x+4)(x-2) = 91

x^2 + 2x - 99 = 0

(x+11)(x-9) = 0

x = 9 <<< answer