Question

A figure is made up of a square and a rectangle. The area of the square is 64 cm². The breadth of the rectangle is the same length of the square. If the total area of the figure is 232 cm², what is the perimeter of the whole figure? ​

Answer 1

90 cm

Explanation:

Let the side of the square be S

Area of the square = S² = 64

So, S = √64 = 8 cm

Let L be the length of the rectangle and B be the breadth

We know B = S = 8

Area of rectangle = BL = 8L

Total area = Area of square + area of rectangle

Total area = 64 + 8L = 232 (given)

Subtracting 64 from both sides yields

8L = 232-64 = 168 or L = 168/8 = 21

Perimeter of square = 4S = 4 x 8 = 32

Perimeter of rectangle = 2(B + L) = 2(8 + 21) = 2 x 29 = 58

Total perimeter = 32 + 58 = 90 cm