SOLUTION: the length of each side of a square is 5 in more than the length of each side of a smaller square. the difference of the areas of the squares is 95in squared. find the lengths of t

Algebra ->  Rectangles -> SOLUTION: the length of each side of a square is 5 in more than the length of each side of a smaller square. the difference of the areas of the squares is 95in squared. find the lengths of t      Log On


   

Question 403311: the length of each side of a square is 5 in more than the length of each side of a smaller square. the difference of the areas of the squares is 95in squared. find the lengths of the sides of the two squares
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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the length of each side of a square is 5 in more than the length of each side of a smaller square.
the difference of the areas of the squares is 95in squared.
find the lengths of the sides of the two squares
:
Let x = side of the smaller square
then
x^2 = area of the smaller square
and
(x+5) = side of the larger square
then
(x+5)^2 = area of the larger square
FOIL this, subtract the smaller square area
x^2 + 10x + 25 - x^2 = 95
x^2 - x^2 + 10x = 95 - 25
10x = 70
x = 7 inches is the side of the smaller square
then
7 + 5 = 12 inches is the side of the larger square
:
:
Check this by finding the areas
12^2 - 7^2
144 - 49 = 95; confirms our solutions