SOLUTION: The longer leg of a right triangle measures two feet more than twice the length of the shorter leg. The hypotenuse measures 3 feet more than twice the shorter leg. Find the length

Question 264476: The longer leg of a right triangle measures two feet more than twice the length of the shorter leg. The hypotenuse measures 3 feet more than twice the shorter leg. Find the length of all three sides.
Answer by CharlesG2(834) (Show Source): You can put this solution on YOUR website!
The longer leg of a right triangle measures two feet more than twice the length of the shorter leg. The hypotenuse measures 3 feet more than twice the shorter leg. Find the length of all three sides.
longer leg b, shorter leg a, hypotenuse c
b = 2a + 2
a
c = 2a + 3
c^2 = a^2 + b^2 (substitute in)
(2a+3)^2 = a^2 + (2a+2)^2 (solve for a)
4a^2 + 12a + 9 = a^2 + 4a^2 + 8a + 4
4a^2 + 12a + 9 = 5a^2 + 8a + 4 (rearrange)
-a^2 + 4a + 5 = 0 (divide both sides by -1)
a^2 - 4a - 5 = 0 (factor)
(a - 5)(a + 1) = 0 (check: a^2 + a - 5a - 5 = a^2 - 4a - 5 used foil)
a can not be -1, so a is 5 so shorter leg is 5 feet
b is 2*5 + 2 or 12 feet
c is 2*5 + 3 or 13 feet

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