Question

Cary told Tony that she wants to build a rectangular patio in her backyard with an area of x^2-3x-10 square feet. If the width needs to be at least 4 feet, what are two sets of possible dimensions for Cary's patio?

Answer 1

we have to factor
x^2 - 3x - 10
= (x-5)(x+2) , the width is x-5 and the length is x+2

so if the width is 5 and the length is 7
area = 5^2 - 3(5) - 10 = 0
so x > 5

let x = 6, then width is 1 and length is 8
let x = 7 , then width is 2 and length is 9
etc.