SOLUTION: I usually am good at this kind of problem, but this one tripped me up a bit! I would really appreciate your help. The question is as follows: The area of a right triangle is 2.

Question 67102: I usually am good at this kind of problem, but this one tripped me up a bit! I would really appreciate your help. The question is as follows:
The area of a right triangle is 2. The sum of the length of the two sides adjacent to the right angle is 10. What is the length of the hypoteneuse of the triangle?
Answer by Nate(3500) (Show Source): You can put this solution on YOUR website!
a = one adj. side
b = different adj. side
Equations:
0.5ab = 2
and
a + b = 10 or a = 10 - b
Plug:
0.5ab = 2
0.5(10 - b)b = 2
10b - b^2 = 4
b^2 - 10b = -4
(b - 5)^2 = 21
b = 5 +- sqrt(21)
Need a positive value:
b = 5 + sqrt(21)
a = 10 - b = 10 - 5 - sqrt(21) = 5 - sqrt(21)
Hypotenuse = c
c^2 = (5 - sqrt(21))^2 + (5 + sqrt(21))^2
c^2 = 25 - 10*sqrt(21) + 21 + 25 + 10*sqrt(21) + 21
c^2 = 92
c = sqrt(92) or about 9.6 units
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