Question

If length of a rectangle is 5 less than 3 times it's breath and perimeter of the rectangle is 22m, then area of the rectangle is:

• A. 28$m^2$
• B. 14$m^2$
• C. 11$m^2$
• D. 21$m^2$

Answer 1

The correct option is A 28$m^2$

Let $l$ and $b$ be the length and breadth of rectangle.

According to the question-

$l=3b-5.....\left(1\right)$

Perimeter of rectangle $=22m\left(\text{Given}\right)$

As we know that the perimeter of rectangle is given as-

$P=2(l+b)$

Therefore,

$2(l+b)=22$

$l+b=11$

$(3b-5)+b=11\left(\text{from}\left(1\right)\right)$

$4b=11+5$

$\Rightarrow b=\frac{16}{4}=4m$

Substituting the value of $b$ in ${eq}^n\left(1\right)$, we have

$l=3\times 4-5=7m$

Therefore,

Area of rectangle $=l\times b=7\times 4=28m^2$

Hence the area of rectangle is $28m^2$.