polynomials in algebra

Question

The area of a gift shop is represented by the expression

4x²-169(in feet)

factor the expression to find the length and width of the shop

Answer 1

169 = 13 squared

4=2 squared

The factors of 4x² - 169 are

(2x-13)(2x+13) a conjugate pair

If the factors are the length and width

then 2x+13 is the length and 2x-13 is the width with 2x>13 or x>13/2 feet

2x+13 > 2x -13 The length is at least 26 feet

L=2x+13 L>26

W=2x-13 W>0

W=2x-13 L=2x+13

W+26=2x+13=L

L=W+26

L is 26 feet longer than the width

Area = A=LW = (W+26)W = W²+26 = 4x²-169 square feet, x>13/2, W>0 L>26, A>0

You need more information to determine unique dimensions W, L or Area