Question 1178858
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