SOLUTION: In a rectangle, one side is 1/3 of the length of the other side and the length of a diagonal is 9 feet, how long are the sides of the rectangle?

Algebra ->  Formulas -> SOLUTION: In a rectangle, one side is 1/3 of the length of the other side and the length of a diagonal is 9 feet, how long are the sides of the rectangle?       Log On


   

Question 1003494: In a rectangle, one side is 1/3 of the length of the other side and the length of a diagonal is 9 feet, how long are the sides of the rectangle?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

one side is 1%2F3 of the length of the other side:
if longer side is a and shorter side is b, then we have:

b=%281%2F3%29a.........eq.1
and if the length of a diagonal is d=9ft, we need to use Pythagorean theorem because two sides of rectangle and its diagonal form right angle triangle
so, we have d%5E2=a%5E2%2Bb%5E2
substitute b from eq.1, and d
%289ft%29%5E2=a%5E2%2B%28%281%2F3%29a%29%5E2........solve for a
81ft%5E2=a%5E2%2B%281%2F9%29a%5E2
81ft%5E2=9a%5E2%2F9%2Ba%5E2%2F9
81ft%5E2=10a%5E2%2F9
81ft%5E2%2A9=10a%5E2
729ft%5E2=10a%5E2
729ft%5E2%2F10=a%5E2
72.9ft%5E2=a%5E2
a=sqrt%2872.9ft%5E2%29
a=8.54ft
then b=%281%2F3%29a=8.54ft%2F3=2.85ft