SOLUTION: The length of the hypotenuse of a right-angled triangle is 17 cm. The base of the triangle is 7 cm more than the height. Find the height of the triangle. I looked at the answer

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Question 401653: The length of the hypotenuse of a right-angled triangle is 17 cm. The base of the triangle is 7 cm
more than the height. Find the height of the triangle.
I looked at the answer from the answers book it said height = 8cm, then I worked out this is because of pythagoras' theorem.
However I don't know how with the information given you would put this in a quadratic equation and work it out, for the question I need to show working out which I am confused of because I don't know the steps of working out, please help.
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
If you recall the 8-15-17 Pythagorean triple, you can conclude the base is 15 and the height is 8.

Or, we can turn this into a quadratic by letting the height be h and the base h+7. Then,

h%5E2+%2B+%28h%2B7%29%5E2+=+17%5E2+=+289

2h%5E2+%2B+14h+%2B+49+=+289

2h%5E2+%2B+14h+-+240+=+0

h%5E2+%2B+7h+-+120+=+0 (dividing by 2)

%28h-8%29%28h%2B15%29+=+0

h = 8 (taking the positive solution).