Question

Sum of the areas of two squares is 850 square m .If the difference of their perimeters is 40m. find the sides of two squares.

Answer 1

Let the sides of the two squares be x and y. Let x > y.

Sum of the areas = 850 m²

⇒ x² + y² = 850   →   (1)

Difference of perimeter of the squares = 40 m

⇒ 4x - 4y = 40 m

⇒ 4(x - y) = 40 m

⇒ x - y = 10 m   →   (2)

Squaring (2),

⇒ (x - y)² = 10²

⇒ x² + y² - 2xy = 100   →   (3)

⇒ 850 - 2xy = 100     [From (1)]

⇒ 2xy = 850 - 100

⇒ 2xy = 750

⇒ xy = 375  

⇒ 4xy = 4 × 375

⇒ 4xy = 1500   →   (4)

(3) + (4)

⇒ x² + y² - 2xy + 4xy = 100 + 1500

⇒ x² + y² + 2xy = 1600

⇒ (x + y)² = 1600

⇒ x + y = 40   ⇒   (5)

(5) + (2)

⇒ (x + y) + (x - y) = 40 + 10

⇒ 2x = 50

⇒ x = 25 m

(5) - (2)

⇒ (x + y) - (x - y) = 40 - 10

⇒ 2y = 30

⇒ y = 15 m

Thus, the sides of each square are 25 m and 15 m long.

Answer 2

HII MATE HERE IS YOUR ANSWER
sum of areas of two squares is 850
let it be that length of 1st square is 'a'
and other square's length is 'b'
area of 1st square is a²
area of 2nd square is b²
sum of the areas of two square is a² + b² = 850
a² + b² = 850 ......... (1)
perimeter of 1st square is 4a
perimeter of 2nd square is 4b
difference of their perimeter is 40
4a - 4b = 40. .............(2)
4a = 40 + 4b
a = 10 + b
put the value in first equation,
( 10 + b) ² + b² =850
100 + 20b + b² + b² = 850
100 + 20b + 2b² = 850
2b² + 20b - 750 = 0
b² +10b - 375 = 0
b² + 25b - 15 b - 375 =0
b( b + 25 ) - 15 ( b + 25) = 0
so that b =15 and -25
length never be negative so that b = 15
a² + b² = 850
a² + 225 =850
a² =850 - 225
a² = 625
a =25
so that length of 1st square is 25
and length of the 2nd square is 15
I HOPE IT WILL HELP YOU