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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