Question

sum of the areas of two squares is 468 m square if the difference of their perimeter is 24 M find the sides of the two squares using quadratic equation

Answer 1

Let the sides of two squares are 'a' and 'b', such that 'a > b'

We are given :-

a² + b² = 468 --- (1)

and, 4a - 4b = 24 => a = 6 + b --- (2)

Now, substituting a = 6 + b in equation - (1)

=> (6 + b)² + b² = 468

=> 36 + b² + 12b + b² = 468

=> 2b² + 12b - 432 = 0

=> b² + 6b - 216 = 0

=> b = {-18, 12}

Since, length can not be negative.

Therefore, b = 12

Then, substituting b = 12 in equation - (2)

=> a = 6 + 12 => a = 18

Thus, a = 18 m and b = 12 m

Hope, it'll help you.....

Answer 2

Hope it helps you!!!