Question

the sum of the areas of two squares is 640 m square at the difference in their perimeter be 64 M find the side of the Other 2 square

Answer 1

Let the sides of squares be x and y
A. To. Q
x²+y²=640--------------------(1)
4x-4y=64
x-y=16
x=y+16
Put x in eq(1)
(16+y)²+y²=640
256+y²+32y+y²=640
2y²+32y-384=0
y²+16y-192=0
y²+24y-8y-192=0
y(y+24)-8(y+24)=0
(y+24)(y-8)=0
y=-24 & y=8
So x=24

Answer 2

Let the side of 1st square = a
and the side of 2nd square = b

according to the question:

a^2 + b^2 = 640 .....(i)eq

&

4a - 4b = 64
4a = 64 - 4b
a = (64 - 4b)/4 ........(ii)eq

put the value of a in eq (i)

{ (64 - 4b)/ 4 }^2 + b^2 = 640

256 + b^2 -32b + b^2 = 640
2b^2 - 32b -384 = 0
b^2 - 16b - 192 = 0

on solving the above equation we get either b=24
or
b= -8

put b in eq (ii)

a = 16 - 24
a = -8