Question

the length of a rectangle is 6 m longer than its width. if the perimeter of the rectangle is 60 m, find its length and width. length: m width: m

Explanation:

Step1: Define variables

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

Step2: Use perimeter formula

The perimeter formula for a rectangle is $P=2(l + w)$. Given $P = 60$ meters, substitute $l=w + 6$ into the formula: $60=2((w + 6)+w)$.

Step3: Simplify the equation

First, simplify the expression inside the parentheses: $60=2(2w + 6)$. Then distribute the 2: $60 = 4w+12$.

Step4: Solve for $w$

Subtract 12 from both sides: $60-12=4w$, so $48 = 4w$. Divide both sides by 4: $w=\frac{48}{4}=12$ meters.

Step5: Solve for $l$

Since $l=w + 6$, substitute $w = 12$: $l=12 + 6=18$ meters.

Answer:

length: 18 m
width: 12 m