SOLUTION: The area of a right triangle is 6. The sum of the lengths of the two sides adjacent to the right angle of the triangle is 12. What is the length of the hypotenuse of the triangle?

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Question 258990: The area of a right triangle is 6. The sum of the lengths of the two sides adjacent to the right angle of the triangle is 12. What is the length of the hypotenuse of the triangle?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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The area of a right triangle is 6.
The sum of the lengths of the two sides adjacent to the right angle of the triangle is 12.
What is the length of the hypotenuse of the triangle?
:
Let x = 1 leg of the right triangle (let it be the base)
then
(12-x) = the other leg (let it be the height)
:
Area: .5*b*h = 6
.5x*(12-x) = 6
6x - .5x^2 = 6
-.5x^2 + 6x - 6 = 0
Multiply by -2
x^2 - 12x + 12 = 0
Using the quadratic formula: x=1.1 and x=10.9, the two sides of the triangle
:
Find the hypotenuse
h = sqrt%281.1%5E2%2B10.9%5E2%29
h = sqrt%281.21%2B118.81%29
h = sqrt%28120.02%29
h = 10.96 is the hypotenuse
:
:
Check by finding the area using the values: .5 * 1.1 * 10.9 = 5.995 ~ 6