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