Answer:
The length of the rug is [tex]7\ ft[/tex]
The width of the rug is [tex]3\ ft[/tex]
Step-by-step explanation:
Let
x----> the length of the rug
y----> the width of the rug
we know that
The area of the rug is
[tex]A=xy[/tex]
[tex]A=21\ ft^{2}[/tex]
so
[tex]21=xy[/tex] -----> equation A
[tex]x=y+4[/tex] -----> equation B
substitute equation B in equation A and solve for y
[tex]21=(y+4)y[/tex]
[tex]y^{2}+4y-21=0[/tex]
Solve the quadratic equation by graphing
The solution is [tex]y=3\ ft[/tex]
see the attached figure
Find the value of x
[tex]x=3+4=7\ ft[/tex]
therefore
The length of the rug is [tex]7\ ft[/tex]
The width of the rug is [tex]3\ ft[/tex]
