Question

The perimeter of the rectangle is 82 m and its area is $400m^2$. The breadth of the rectangle is ___ .

• A. 16 m
• B. 14 m
• C. 18 m
• D. 10 m

Answer 1

The correct option is A

16 m

Given that 2(l + b) = 82 ____(1)

and l $\times$ b = 400

b = $\frac{400}{l}$

Substituting b in (1)
$2(l+\frac{400}{l})=82$
$l+\frac{400}{l}=41$
$l^2+400=41l$
$l^2-41l+400=0$
$l^2-25l-16l+400=0$
$l(l-25)-16(l-25)=0$
$(l-25)(l-16)=0$
$\Rightarrow l=25andl=16$
$\therefore 2(l+b)=82$
$(25+b)=41$ (Longer side of the rectangle is taken as its length)
$b=41-25$
$b=16m$