Question

Sum of the area of two squares is 260. if the difference of their perimeter is 24cm then find the sides of the two square

Answer 1

let the sides of square be x and y

then their peimeters are 4x and 4y and areas be x2 and y2

a/q

x2+y2=260...........(1) 

also,

4x-4y=24

4(x-y)=24

x-y=6..........(2)

 

(x+y)2 +(x-y)2 =2(x2+y2)

(x+y)2 +(6)2 =2(260)

(x+y)2 + 36=520

(x+y)2=520-36=484

x+y=22.............(3)

now adding eqn. 2 and 3...........

x-y+x+y=6+22

2x=28

x=14

y=22-x=22-14=8

hope that it helps. . . . . .