Question

the sum of the areas of two squares is 640 CM square if the difference between their perimeter is 64 CM then find side of the square​

Answer 1

let the side of both squares be a and b respectively.

Sum of areas = (a^2 + b^2) = 640cm....(1)

difference between perimeter is 4(a-b)=64

* (a-b) = 16 cm

so, a= 16+b cm

Substitute it in (1)

(16+b)^2 + b^2 = 640

256 + 32b +b^2 +b^2 = 640

2b^2 + 32b - 384 =0

b^2 + 16b - 192 = 0

b^2 + 24b - 8b -192 = 0

b(b+24) - 8(b+24)

so, b=8

so, a^2 + 64 = 640

a^2 = 576

a= 24

so, b=8, a=24