Question

the length of a rectangle is 4 m longer than its width. if the perimeter of the rectangle is 48 m, find its area.

Explanation:

Step1: Let the width be $x$ meters.

The length is $x + 4$ meters.

Step2: Use the perimeter formula.

The perimeter formula of a rectangle is $P=2(l + w)$. Given $P = 48$ meters, so $2(x+(x + 4))=48$.
First, simplify the left - hand side: $2(2x + 4)=48$. Then expand to get $4x+8 = 48$.
Subtract 8 from both sides: $4x=48 - 8=40$.
Divide both sides by 4: $x = 10$ meters.

Step3: Find the length.

The length $l=x + 4=10 + 4 = 14$ meters.

Step4: Calculate the area.

The area formula of a rectangle is $A=l\times w$. So $A=14\times10 = 140$ square meters.

Answer:

$140$