SOLUTION: One leg of a right triangle is 1cm longer than the other leg. the length of the hypotenuse is 9cm greater than that of the shorter leg. Find the lengths of the three sides.
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Question 312185: One leg of a right triangle is 1cm longer than the other leg. the length of the hypotenuse is 9cm greater than that of the shorter leg. Find the lengths of the three sides. Answer by fractalier(6550) (Show Source):
You can put this solution on YOUR website! Let x be the length of the shortest leg.
Then x+1 is the length of the other leg.
And x+9 is the length of the hypotenuse.
Now apply the Pythagorean Theorem: a^2 + b^2 = c^2 and get
x^2 + (x+1)^2 = (x+9)^2
Now expand, collect like terms and solve for x...
x^2 + x^2 + 2x + 1 = x^2 + 18x + 81
x^2 - 16x - 80 = 0 (This can be factored, luckily)
(x - 20)(x + 4) = 0 and thus
x = 20
x+1 = 21 and
x+9 = 29
The sides are 20, 21, and 29.
