A rug has an area of x2+x-20 square feet. Which expression represents the dimensions of the rug? A (x+4) (x-5) B (x+2) (x-10) C (x-4) (x+5) D (x-2) (x+10)

Question

Rylee Key

Mathematics

11 January, 02:03

A rug has an area of x2+x-20 square feet. Which expression represents the dimensions of the rug? A (x+4) (x-5) B (x+2) (x-10) C (x-4) (x+5) D (x-2) (x+10)

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Answers (1)

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Tripp French · Answer 1

Answer: the correct option is

C (x-4) (x+5)

Step-by-step explanation:

The area of the rug in square feet is expressed as

x^2+x-20

The given equation is a quadratic equation and the roots of the equation represents the dimensions of the rug. To simplify the equation, we would apply the factorization method.

We will get two numbers such that, their difference will be x and their sum will be - 20x^2. The numbers are 5x and 4x. Therefore

x^2 + 5x - 4x - 20 = 0

x (x + 5) - 4 (x + 5)

The roots are (x - 4) (x + 5)