Question

The length of a rectangle exceeds the breadth by $3\text{m}$ and the perimeter is $5$ times the breadth. Find the length, breadth and perimeter of the rectangle.

Answer 1

l=length b-breadth

from $1^{st}$ condition

$l=b+3$ _______ (1)

perimeter of rectangle = 2(l+b)

from $2^{nd}$ condition

$2(l+b)=5b$

$2l+2b=5b$

$2l=3b$

$l=\frac{3b}{2}$ putting in equation (1)

$\frac{3b}{2}=b+3$

$\frac{3b}{2}-b=3$

$\frac{b}{2}=3$ $\therefore b=6m$ $\therefore l=b+3=6+3=9m$

perimeter = 2(l+b)

= 2(9+6)=30 m.