Question

the length of a rectangle is five times its width. if the perimeter of the rectangle is 72 yd, find its length and width. length: yd width: yd

Explanation:

Step1: Define variables

Let the width of the rectangle be $w$ yards. Then the length $l = 5w$ yards.

Step2: Use perimeter formula

The perimeter formula of a rectangle is $P=2(l + w)$. Substitute $l = 5w$ and $P = 72$ into the formula: $72=2(5w+w)$.

Step3: Simplify the equation

First, simplify the right - hand side of the equation: $72=2(6w)=12w$.

Step4: Solve for $w$

Divide both sides of the equation $72 = 12w$ by 12: $w=\frac{72}{12}=6$ yards.

Step5: Solve for $l$

Since $l = 5w$, substitute $w = 6$ into the equation: $l=5\times6 = 30$ yards.

Answer:

length: 30 yd
width: 6 yd