Question

two squares have a total area of 208cm square and sum of their perimeter is80cm what are the length of sides of square

Answer 1

The length of the sides of the square are 8 centimetres and 12 centimetres respectively

How to finds area of a square?

area = l²

where

• l = side length

Therefore,

x² + y² = 208

How to finds perimeter of a square?

perimeter = 4l

4x + 4y = 80 cm

x + y = 20

x = 20 - y

(20 - y)² + y² = 208

y² - 40y + 400 + y² = 208

2y² - 40y + 192

y² - 20y + 96

(y - 12)(y - 8)

Therefore, y  = 12 and y = 8

when y = 8

x + 8 = 20

x = 12

when y = 12

x + 12 = 20

x = 8

Therefore, the length of the sides of the square are 12 cm and 8 cm.

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