Question

A rectangle’s length is 8 feet shorter than four times its width. The rectangle’s perimeter is 134 feet. Find the rectangle’s length and width.

The rectangle’s length is ____ feet, and its width is _____ feet.

Answer 1

length= 52 feet,

width= 15 feet

Explanation:

Let the length and the width of the rectangle bs L and W feet respectively.

L= 4W -8 -----(1)

Perimeter of rectangle= 2(length +width)

2(L +W)= 134

Divide both sides by 2:

L +W= 67 -----(2)

`\textcolor{steelblue}{\text{\textcircled{2} Solve for one variable}}`

Substitute (1) into (2):

4W -8 +W= 67

5W -8= 66

5W= 67 +8

5W= 75

W= 75 ÷5

W= 15

`\textcolor{steelblue}{\text{\textcircled{3} Solve for the other variable}}`

Substitute W= 15 into (1):

L= 4(15) -8

L= 60 -8

L= 52

`\textcolor{steelblue}{\text{\textcircled{4} Write concluding statement}}`

Thus, the rectangle's length is 52 feet, and its width is 15 feet.