Question

Mrs. Harbrook can choose from two rectangular pool sizes. The pool manufacturer provides her with the area of the pool, but she needs to find the dimensions in order to determine if the pool will fit in her yard.

If the area of the pool is x2−17x+72, what are possible expressions to represent the length L and the width W ?

Answer 1

Answer:8 or 9 ft

Explanation:

Given

The area of the pool is
`A=x^2-17x+72`

The area is in the form of a quadratic equation

So, the roots of the equation will give the length and width of the pool

`\Rightarrow x^2-17x+72=0\\\Rightarrow x^2-8x-9x+72=0\\\Rightarrow x(x-8)-9(x-8)=\\\Rightarrow (x-8)(x-9)=0\\\Rightarrow x=8\ or\ 9`

Therefore length and width can either be
`\text{8 or 9 ft}`.

`\Rightarrow L=8\ ft,W=9\ ft\ \text{or}\ L=9\ ft,W=8\ ft`