Question

The sum of areas of two squares is 468m²
If the difference of their perimeter is 24cm.
find the sides of two square ..​

Answer 1

Answer:

Sides of two squares are 18 & 12

Step-by-step explanation:

Let sides of two squares be x & y

given sum of areas of two squares = 468

=> x^2+y^2 = 468

Difference of. their perimeters = 24cm

=> 4x-4y = 24 => x-y = 24/4

=> x-y = 6...............(1)

we know that (x-y)^2 = x^2+y^2-2xy

=> (6)^2 = 468-2xy

=> 36 = 468-2xy

=> 2xy = 468-36

=> 2xy = 432

=> xy = 216

Let (x+y)^2 = x^2+y^2+2xy

= 468+(2×216)

= 468+432

= 900

x+y = (900)^(1/2)

x+y = 30..............(2)

Add (1) & (2)

(x-y)+(x+y) = 6+30

2x = 36

x = 36/2 = 18

from (2)

18+y = 30

y = 30-18 = 12

.·. Sides of two squares are 18 & 12