Question

the length of a rectangle is 3 m longer than its width. if the perimeter of the rectangle is 66 m, find its length and width. length: m width: m

Explanation:

Step1: Define variables

Let the width of the rectangle be $x$ m. Then the length is $(x + 3)$ m.

Step2: Use perimeter formula

The perimeter formula of a rectangle is $P=2(l + w)$. Given $P = 66$ m, we have $66=2((x + 3)+x)$.

Step3: Simplify the equation

First, simplify the equation inside the parentheses: $66=2(2x + 3)$. Then distribute the 2: $66 = 4x+6$.

Step4: Solve for $x$

Subtract 6 from both sides: $66-6=4x$, so $60 = 4x$. Divide both sides by 4: $x=\frac{60}{4}=15$.

Step5: Find length and width

The width $x = 15$ m. The length is $x + 3=15 + 3=18$ m.

Answer:

length: 18 m
width: 15 m