Two squares have an average perimeter of 36 and an average area of 90. What is the side length of the larger square?

2 answers

side of first square ---- x
side of 2nd square ----- y

(4x + 4y)/2 = 36
x+y = 18 --- y = 18-x

(x^2 + y^2)/2 = 90
x^2 + y^2 = 180
x^2 + (18-x)^2 = 180
x^2 + 324 - 36x + x^2 = 180
x^2 - 18x + 72 = 0
(x - 12)(x - 6) = 0
x=12 or x=6

if x=12, then y = 6
if x = 6 , then y = 12

we have symmetric solutions

the side of the larger square is 12
The perimeter of two squares is 58in. The side length of the larger square is twice the side length of the smaller square. What is is the length of one side of the smaller square?