Question

A wire of length 21 cm is bent in the form of a rectangle in such a way that its length becomes $1\frac{1}{2}$ less than twice its breadth. Find the length and the breadth of the rectangle.

Answer 1

The bent wire becomes the perimeter of the rectangle $=2(l+b)=21$

Let the breadth be $x$

then its length $=2x-1.5$

Perimeter $=2(2x-1.5+x)=21$

$\Rightarrow 2(3x-1.5)=21$

$\Rightarrow 6x-3=21$

$\Rightarrow 6x=21+3$

$\Rightarrow 6x=24$

$\Rightarrow x=\frac{24}{6}=4$

$\therefore$Breadth $=4cm$

and length $=2x-1.5=2\times 4-1.5=8-1.5=6.5cm$