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

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) (Show Source): You can put this solution on YOUR website!
Let the shortest side be x
Then the hypotenuse is
3rd side is
Pythagoras theorem:
Square of hypotenuse = sum of squares of other 2 sides.
So,
Expanding:

[Using the formulae for ]
Simplifying:
, 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.

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