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

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 $(10x-6)$

Answer 2

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