SOLUTION: I'm in college and I have a question on my math homework and its asking me for the area of a triangle and all the lengths of the sides and its only telling me that the hypotenuse i

Question 988275: I'm in college and I have a question on my math homework and its asking me for the area of a triangle and all the lengths of the sides and its only telling me that the hypotenuse is 3 cm longer than the long side, and the short side is 3 cm shorter than the long side. can you just show me how to set this up?
Answer by Cromlix(4381) (Show Source): You can put this solution on YOUR website!
Hi there,
Make the long side = 'x'
Hypotenuse = x + 3
Short side = x - 3
Now by Pythagoras
(long side)^2 + (short side)^2 = (hypotenuse)^2
(x)^2 + (x - 3)^2 = (x + 3)^2
Working out equations;
x^2 + x^2 - 6x + 9 = x^2 + 6x + 9
Collect like terms
x^2 + x^2 - x^2 - 6x - 6x + 9 - 9 = 0
x^2 - 12x = 0
x(x - 12) = 0
x = 12.
So,
Hypotenuse = 15cm
Long side = 12cm
Short side = 9cm
Area of triangle = 1/2(base x height)
Area of triangle = 1/2 (12 x 9)
Area of triangle = 1/2(108)
Area of triangle = 54cm^2
Hope this helps :-)
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