Question

A rectangle has adjacent sides 8 cm and 6 cm. The perimeter of the square is equal to the perimeter of this rectangle find the difference between the area of the square and that of rectangle.

Answer 1

Length (l) of the rectangle = 8 cm
Breadth (b) of the rectangle = 6 cm
Let the side of the square be a cm.
Give:
Perimeter of the square = perimeter of the rectangle
$\Rightarrow$4 × a = 2 (l + b)
$\Rightarrow$4 × a = 2 (8 + 6)
$\Rightarrow$4 × a = 28
$\Rightarrow$a = 7
$\Rightarrow$Side of the square = 7 cm

Difference between the areas of the square and the rectangle = area of the square − area of the rectangle
= {(a)² – lb} cm²
= {(7)² – (8)(6)} cm²
= (49 – 48) cm²
= 1 cm²
Thus, the difference is 1 cm².