Answer:
The length of the rectangle is 24 inches and the width is 7 inches
Step-by-step explanation:
Let
x ----> the length of rectangle
y ----> the width of rectangle
we know that
The perimeter of rectangle is equal to
[tex]P=2(x+y)[/tex]
we have
[tex]P=62\ in[/tex]
so
[tex]62=2(x+y)[/tex]
[tex]31=x+y[/tex] ----> equation A
[tex]y=\frac{1}{4}x+1[/tex] ---> equation B
Solve the system by substitution
substitute equation B in equation A
[tex]31=x+\frac{1}{4}x+1[/tex]
solve for x
[tex]\frac{5}{4}x=30[/tex]
[tex]x=30(4)/5\\x=24[/tex]
Find the value of y
[tex]y=\frac{1}{4}(24)+1\\\\y=7[/tex]
therefore
The length of the rectangle is 24 inches and the width is 7 inches
