SOLUTION: Find the lengths of the sides of a right triangle if we know that the longer leg is 2 feet longer than the shorter leg, while the hypotenuse is 5 feet longer than the shorter leg.

Algebra ->  Graphs -> SOLUTION: Find the lengths of the sides of a right triangle if we know that the longer leg is 2 feet longer than the shorter leg, while the hypotenuse is 5 feet longer than the shorter leg.       Log On


   

Question 971362: Find the lengths of the sides of a right triangle if we know that the longer leg is 2 feet longer than the shorter leg, while the hypotenuse is 5 feet longer than the shorter leg. Sketch and label the triangle, set up the equation that models the relationship and then solve
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the shorter leg is x
the longer leg is x+2
the hypotenuse is x+5
by pythagorus:
a^2 + b^2 = c^2 which results in
x^2 + (x+2)^2 = (x+5)^2
solve that equation using the quadratic formula to get x = 8.477225575 or a negative number that is invalid because the length of a side can't be negative.
the length of the shorter leg is 8.477225575.
the length of the longer leg is 10.477225575.
the length of the hypotenuse is 13.477225575.
a^2 + b^2 + c^2 becpomes:
8.477225575^2 + 10.477225575^2 = 13.477225575^2 which becomes:
181.6356091 = 181.6356092 which is true.