Question

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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

Answer:

The length side of the original square banner was 9 ft

Step-by-step explanation:

Let

x-----> the length side of the original square banner

we know that

The new area of the banner is equal to

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

Solve for x

$91=(x+4)(x-2)\\ \\91=x^{2}-2x+4x-8\\ \\x^{2}+2x-99=0$

Solve the quadratic equation by graphing

The solution is x=9 ft

see the attached figure

Answer 2

The length of the  original square banner is 9feet

How to find the side length of the banner

Let the original side length of the banner be "x"

If the square banner had 4 feet added its width and 2 feet subtracted from its height with an area of 91 square feet, then;

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

Factorize

x^2 + 2x - 8 = 91

x^2 + 2x - 99 = 0

x^2 + 11x - 9x - 99 = 0

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

x - 9 = 0

x = 9

Hence the length of the  original square banner is 9feet

Learn more on area of square here: https://brainly.com/question/11444061