SOLUTION: The hypotenuse of a right triangle is 17 cm long. Another side of the triangle is 7 cm longer than the third side. Determine the unknown side lengths.

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Question 814762: The hypotenuse of a right triangle is 17 cm long. Another side of the triangle is 7 cm longer than the third side. Determine the unknown side lengths.
Answer by gsmani_iyer(201) About Me  (Show Source):
You can put this solution on YOUR website!
Let one side = x cm. Then,
Second side = x + 7 cm.
Hypotenuse = 17 cm. (Given)
According to the Pythagoras theorem,
17%5E2+=+x%5E2+%2B+%28x%2B7%29%5E2

= 289+=+x%5E2+%2B+x%5E2+%2B+14x+%2B+49
= 289+=+2x%5E2+%2B+14x+%2B+49
= 2x%5E2%2B14x%2B49+=+289
= 2x%5E2%2B14x+=+289-49
= 2x%5E2%2B14x+=+240 Dividing this equation by 2, we get
= x%5E2%2B7x+=+120
= x%5E2%2B7x-120+=+0
= %28x%2B15%29%28x-8%29+=+0. So, either (x+15) or (x-8) = 0.
So, x = -15 or x = 8. But x cannot be equal to -15 as it is not a real No.
So, highlight%28x+=+8%29. So one side = 8 cm. and another side = 15.
I think, it is clear to you now. All the best. Feel free to contact me at gsmani9@yahoo.com as I am a home tutor in India.