Answer:
Length [tex]14\ cm[/tex]
Width [tex]3\ cm[/tex]
Step-by-step explanation:
Let
x-----> the length of rectangle
y ----> the width of rectangle
we know that
The area of rectangle is equal to
[tex]A=xy[/tex]
[tex]A=42\ cm^{2}[/tex]
so
[tex]42=xy[/tex] ----> equation A
[tex]x=2y+8[/tex] ---> equation B
substitute equation B in equation A and solve for y
[tex]42=(2y+8)y\\ \\2y^{2}+8y-42=0[/tex]
Solve the quadratic equation by graphing
The solution is [tex]y=3\ cm[/tex]
see the attached figure
Find the value of x
[tex]x=2(3)+8=14\ cm[/tex]
therefore
Length [tex]14\ cm[/tex]
Width [tex]3\ cm[/tex]
