Question

the length of a rectangle is six times its width. if the perimeter of the rectangle is 126 ft, find its length and width. length: ft width: ft

Explanation:

Step1: Define variables

Let the width of the rectangle be $w$ feet. Then the length $l = 6w$ feet.

Step2: Use perimeter formula

The perimeter formula for a rectangle is $P=2(l + w)$. Substitute $l = 6w$ and $P = 126$ into the formula: $126=2(6w+w)$.

Step3: Simplify the equation

First, simplify the right - hand side: $126 = 2(7w)=14w$.

Step4: Solve for $w$

Divide both sides of the equation $126 = 14w$ by 14: $w=\frac{126}{14}=9$ feet.

Step5: Solve for $l$

Since $l = 6w$, substitute $w = 9$ into the equation: $l=6\times9 = 54$ feet.

Answer:

length: 54 ft
width: 9 ft