Answer:
Length: 40 inches
Width: 10 inches
Step-by-step explanation:
Let [tex]x =[/tex] width of the rectangle.
From the information "length of a rectangle is four times its width", we can express the length as:
Length = [tex]4x[/tex]
- - - -
Perimeter = [tex]2l+2w[/tex] (formula for perimeter of rectangle)
[tex]100=2(4x)+2(x)[/tex]
[tex]100=8x+2x[/tex]
[tex]10x=100[/tex] (combine like terms)
[tex]x=10[/tex] inches
∴ The width of the rectangle is 10 inches.
To find the length of the rectangle, we can use substitution:
Length = [tex]4x[/tex]
[tex]=4(10)[/tex]
[tex]=40[/tex] inches
∴ The length of the rectangle is 40 inches.
Hope this helps :)
