Question

The perimeters of five squares are 24 cm, 32 cm, 40 cm, 76 cm and 80 cm respectively. The perimeter of another square equal in area to the sum of the area of these squares is:

• A. 31 cm
• B. 62 cm
• C. 124 cm
• D. 961 cm
• E. None of these

Answer 1

The correct option is C

124 cm

The sides of the five squares are $\left(\frac{24}{4}\right),\left(\frac{32}{4}\right),\left(\frac{40}{4}\right),\left(\frac{76}{4}\right),\left(\frac{80}{4}\right)$ i.e., 6 cm, 8 cm, 10 cm, 19 cm, 20 cm.
$\therefore$ Area of the new square = [6${}^2$ + 8${}^2$ + (10)${}^2$ + (19)${}^2$ + (20)${}^2$] = (36 + 64 + 100 + 361 + 400) cm${}^2$ = 961 cm${}^2$
Side of the new square = $\sqrt{961}cm$ = 31 cm
Perimeter of the new square = (4 $\times$ 31) cm = 124 cm