Question

A wire is bent in the shape of a rectangle. Its length is $36$cm and breadth is $25$cm. If the same wire is bent in the shape of a square, what will be the measure of its side? Among these two shape which shape occupies more area?

Answer 1

Given

Case I : A wire is bent in shape of rectangle.

$length=36cm$

$Breath=25cm$

Total length of wire is $=$ Perimeter of rectangle

$=2(l+b)$

$=2[36+25]$

$\Rightarrow 2\left(61\right)=122cm$

length of wire $=122cm$

Area occupied by wire $=l\times b=36\times 25$

$\Rightarrow A_R=900c{m}^2$

Case II: If this wire is bent in shape of square then,

length of wire $=$ Perimeter of square

$122=4a$

$a=\frac{122}{4}=\frac{61}{2}cm$

Now area of wire is shape of square $=a^2$

$A_s={\left(\frac{61}{2}\right)}^2=930.25c{m}^2$

Hence the wire is bent in shape of square then it has each side of $30.5cm$ each

And square shape occupies more area.

$A_s=930.25c{m}^2$