Question

The perimeter of a square-shaped lawn is 96 cm. The breadth of a rectangular-shaped lawn is 16 cm. If the area of the rectangle-shaped lawn is 16 $c{m}^2$ less than the area of the square-shaped lawn, what is the perimeter of the rectangular lawn?

• A. 100 cm
• B. 102 cm
• C. 104 cm
• D. 106 cm

Answer 1

The correct option is B 102 cm

Given, the perimeter of the square-shaped lawn = 96 cm
Perimeter of the square = 4 x side
$\Rightarrow$ 4 x side = 96 cm
$\Rightarrow$ side = 24 cm
Thus, area of the square-shaped lawn = $(side{)}^2$ = $(24cm{)}^2$ = 576 $c{m}^2$

As per the given data,
Area of the rectangular-shaped lawn = Area of the square-shaped lawn - 16 $c{m}^2$
= 576 $c{m}^2$ - 16 $c{m}^2$
= 560 $c{m}^2$

Now, breadth of the rectangular-shaped lawn = 16 cm
Area of a rectangle = length x breadth
$\Rightarrow$ 560 $c{m}^2$ = length x 16 cm
$\Rightarrow$ length = 35 cm

Perimeter of a rectangle = 2 (length + breadth)
Hence, the perimeter of the rectangular-shaped lawn
= 2 x (35 cm + 16 cm)
= 2 x 51 cm
= 102 cm