Question

sum of area of 2 squares is 850m^2. If the difference of their perimeters is 40m,find their sides​

Answer 1

Area of 1 square = a²

Area of 2 square = b²

It is given that ,

a² + b² = 850 m²

=> a² + b² = 850 ... (i)

Perimeter of 1 square = 4a

Perimeter of 2 square = 4b

4a - 4b = 40

4 ( a - b ) = 40

a - b = 10

a = 10 + b ....(ii)

Put value of a in (i)

a² + b² = 850

=> (10 + b)² + b² = 850

=> 100 + b² + 20b + b² = 850

=> 2b² + 20b = 750

=> 2b² + 20b - 750 = 0

=> 2 (b² + 10b - 375 ) = 0

=> b² + 10b - 375 = 0

=> b² + 25b - 15b - 375 = 0

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

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

=> b = -25 or b = 15

Taking positive value of b = 15,

Putting the value of b in (ii)

a = 10 + b

=> a = 10 + 15

=> a = 25

Hence , the sides if two squares are 15 m and 25 m respectively.

#sumedhian ❤❤

Answer 2

Step-by-step explanation:

let the side of first square=x

let the side of second square=y

x²+y²=850

4x-4y=40

4(x-y)=40

x-y=40/4

x-y=10

x=10+y

(10+y)²+y²=850

100+y²+20y+y²=850

2y²+20y-750=0

2(y²+10y-375)=0

y²+10y-375=0

y=15

x=10+y

x=25

x=25. y=15