SOLUTION: A right triangle's hypotenuse is 1 cm longer than twice the length of the shortest side. The third side is 1 cm less than twice the shortest side. Find the length (in cm) of the h

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: A right triangle's hypotenuse is 1 cm longer than twice the length of the shortest side. The third side is 1 cm less than twice the shortest side. Find the length (in cm) of the h      Log On


   

Question 760230: A right triangle's hypotenuse is 1 cm longer than twice the length of the shortest side. The third side is 1 cm less than twice the shortest side.
Find the length (in cm) of the hypotenuse?
Answer by ramkikk66(644) About Me  (Show Source):
You can put this solution on YOUR website!
Let the shortest side be x
Then the hypotenuse is 2%2Ax+%2B+1
3rd side is 2%2Ax+-+1
Pythagoras theorem:
Square of hypotenuse = sum of squares of other 2 sides.
So, %282x+%2B+1%29%5E2+=+x%5E2+%2B+%282x+-+1%29%5E2
Expanding:
4x%5E2+%2B+4x+%2B+1+=+x%5E2+%2B+%284x%5E2+-+4x+%2B+1%29
[Using the formulae for %28a%2Bb%29%5E2+=+a%5E2%2B2ab%2Bb%5E2]
Simplifying:
4x+=+x%5E2+-+4x, or
4 = x - 4.
i.e. x = 8.
So, the 3 sides are 8, 15 and 17 (hypotenuse)
To check, apply the pythagoras theorem.
8^2 = 64 (square of 1 side)
15^2 = 225 (square of the 2nd side)
17^2 = 289 (square of hypotenuse)
64 + 225 = 289, so the answer is correct. Length of hypotenuse = 17 cm.