The length of a rectangle is 10 cm more than the side of a square and its breadth is 8 cm less than the side of the square. If the areas of both the rectangle and square are equal, then what will be the perimeter (in cm) of the rectangle?

164

We know that,

Area of square = (Side)²

Area of rectangle = l × b

Perimeter of rectangle = 2(l + b)

The length of rectangle = 10 cm more than the side of square

The breadth of rectangle = 8 cm less than the side of the square

Let the side of square be s 

According to the question

= (s + 10)(s – 8) = s²

= 2a – 80 = 0

= 2s = 80

= s = 40 cm

Length = (40 + 10) = 50 cm

Breadth = (40 – 8) = 32 cm

Perimeter of rectangle = 2(l + b)

= 2(50 + 32)

= 2 × 82 = 164 cm