Question 1178858: The hypotenuse of a right triangle
is 3cm longer than one of its legs
and 6cm longer than its other leg.
What is the area of the triangle?
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! Let x = the length of the hypotenuse
Then one of the legs is x-3 and the other leg is x-6
Since the triangle is a right triangle, using the Pythagorean theorem we have:
(x-3)^2 + (x-6)^2 = x^2 -> x^2 - 18x + 45 = 0
This can be factored as:
(x-3)(x-15) = 0
The solutions are x = 3 and x = 15. The answer cannot be x = 3, since that would
make the legs 0 and -3.
Thus, x = 15. Therefore the area is 1/2*(12)(9) = 54 cm^2
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