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? 9x 4 10x – 19 10x – 6 8x – 6

Answer 1

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

Explanation:

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*WA=L∗W

A= 120x^{2} + 78x - 90A=120x

2

+78x−90

L=12x+15L=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=0120x

2

+78x−90=0

using a graph tool

see the attached figure

\begin{gathered} x=-1.25\\ x=0.6\end{gathered}

x=−1.25

x=0.6

120x^{2} + 78x - 90=120*(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)120∗(x+1.25)∗(x−0.6)=6∗(4x+5)∗(5x−3)

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

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

therefore

the answer is

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