Question 378931
The sum of the areas of two squares is 4,477 square inches.
 Each side of the larger square is 6 times the length of a side of the smaller square.
 Find the length of a side of the smaller square. 
:
Let x = side of the small square
then
6x = side of the large square
:
Large sq area + small sq area = 4477
(6x)^2 + x^2 = 4477
36x^2 + x^2 = 4477
37x^2 = 4477
Divide both sides by 37, results
x^2 = 121
x = {{{sqrt(121)}}}
x = 11 inches is the side of the smaller square
:
:
Check solution by finding the total area
66^2 + 11^2 =
4356 + 121 = 4477, confirms our answer