Sum of areas of two squares is 400 cm². If the difference of their parameters is 16 cm, find the sides of two squares.

To find: Sides of two squares

Method Used:

To solve the quadratic equation by factorisation method, follow the steps:

1) Multiply the coefficient of x² and constant term.

2) factorise the result obtained in step 1.

3) Now choose the pair of factors in such a way that after adding or subtracting(splitting) them

You get coefficient of x.

Explanation:

Let side of first square be “a”

And side of second square be “b”.

As area of square = side²

Perimeter of square = 4×side

According to question:

a² + b² = 400 …. (1)

Also,

4a – 4b = 16

⇒ a – b = 4

⇒ a = b + 4 …. (2)

Put this value in (1) to get,

(b+4)² + b² = 400

Apply the formula (a + b)² = a² + b² + 2ab

⇒ b² + 16 + 8b + b² = 400

⇒ 2b² + 16 – 400 + 8b = 0

⇒ 2b² + 16 – 400 + 8b = 0

⇒ 2b² – 384 + 8b = 0

⇒ b² + 4b – 192 = 0

Split the middle term:

⇒ b² + 16b – 12b – 192 = 0

⇒ b (b + 16) – 12(b+16) = 0

⇒ (b-12) (b+16) = 0

⇒ b = 12 and b = - 16

As side of the square cannot be negative,

So, b = 12

From (2),

a = b + 4

= 12 + 4

= 16

Hence sides of both squares are 16 cm and 12 cm.