Question

the length of a rectangle is 6 m longer than its width. if the perimeter of the rectangle is 40 m, find its area.

Explanation:

Step1: Define variables

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

Step2: Use the perimeter formula

The perimeter formula of a rectangle is $P=2(l + w)$. Given $P = 40$ m, we substitute $l$ and $P$ into the formula: $40=2((w + 6)+w)$.
Simplify the right - hand side: $40=2(2w + 6)$.
Expand: $40 = 4w+12$.
Subtract 12 from both sides: $4w=40 - 12=28$.
Divide both sides by 4: $w = 7$ m.

Step3: Find the length

Since $l=w + 6$, substituting $w = 7$ m, we get $l=7 + 6=13$ m.

Step4: Calculate the area

The area formula of a rectangle is $A=l\times w$. Substitute $l = 13$ m and $w = 7$ m: $A=13\times7 = 91$ $m^{2}$.

Answer:

$91$