Q. 243.7( 3 Votes )

# Sum of areas of t

Answer :

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.

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