Question

The area, A, of a rectangle is 120x2 + 78x – 90, and the length, l, of the rectangle is 12x + 15. Which of the following gives the width, w, of the rectangle?

A.9x + 4
B.10x – 19
C.10x – 6
D.8x – 6

Answer 1

The answer will be C. 10x -6
(10x-6)(12x+15)=120x^2+78x-90

Answer 2

Let

L--------> the length side of a rectangle

W--------> the width side of a rectangle

we know that

the area of a rectangle is equal to

`A=L*W`

`A= 120x^(2) + 78x - 90`

`L=12x+15`

To find the width side W of the rectangle we need to find the roots of the equation of the area

so

Equate to zero the area and find the roots

`120x^(2) + 78x - 90=0`

using a graph tool

see the attached figure

`x=-1.25\\ x=0.6`

`120x^(2) + 78x - 90=120*(x+1.25)*(x-0.6)`

`120*(x+1.25)*(x-0.6)=6*(4x+5)*(5x-3)`

`6*(4x+5)*(5x-3)=3*(4x+5)*2*(5x-3)`

`3*(4x+5)*2*(5x-3)=(12x+15)*(10x-6)`

therefore

the answer is

the width of the rectangle is equal to
`(10x-6)`