Question

sum of the areas of two squares is 850 m square if the difference of their perimeter is 40 metres find the sides of the two squares​

Answer 1

Let sides of 2 squares be a and b

areas of 2 squares are a^2 and b^2

As sum of areas is 850

So a^2 + b^2 = 850

Perimeter of 2 squares are 4a and 4b

Asdifference of perimeters is 40

4 a - 4b = 40 ( a>b)

4( a- b) = 40

a- b= 10

a= 10 + b

and a^2+ b^2 = 850

( 10+ b)^2 + b^2 = 850

100 + b^2 + 20 b + b^2 -850= 0

2 b^2 + 20 b - 750 = 0

b^2 + 10 b - 375 = 0

b^2 +25b - 15 b-375 = 0

b( b+25) -15( b+25)= 0

( b-15)(b+25)= 0

b= 15, -25

neglect b= -25

So b= 15

So a = 10 + b= 10+15= 25

SO

sides of 2 squares are15 and 25

✌✌✌Dr.Dhruv✌✌✌✌