Question

Question 101

A large square is made by arranging a small square surrounded by four congruent rectangles as shown in the given figure. If the perimeter of each of the rectangle is 16 cm, find the area of the large square.

Answer 1

Let the length and breadth of the rectangle be l and b, respectively.

It is given that, perimeter of one rectangle = 16 cm
$\Rightarrow 2(l+b)=16[\because$ perimeter of rectangle =2(l+b)]
$\Rightarrow l+b=8cm$
Since, the side of larger square is (l+b).
Hence, area $=(side{)}^2=(l+b{)}^2=(8{)}^2=64c{m}^2$