Question

Sum of the areas of two squares is 400cm^2. If the difference of their perimeter is 16cm, find the sides of the two squares.

Answer 1

The sides are 12 cm and 16 cm long.

Explanation:

x^2 + y^2 = 400 where a and y are the sides of the squares.

4x - 4y = 16 (The difference of the perimeters).

x - y = 4

x = 4 + y.

Substitute for x in the first equation:

(4 + y)^2 + y^2 = 400

16 + 8y + y^2 + y^2 = 400

2y^2 + 8y - 384 = 0

y^2 + 4y - 192

(y - 12)(y + 16) = 0

y = -16, 12 We ignore the negative root:

y = 12 .

and x = 4 + y = 16.