SOLUTION: The area of a right triangle is 4 . The sum of the lengths of the two sides adjacent to the right angle of the triangle is 9 . What is the length of the hypotenuse of the triangle?

Algebra ->  Triangles -> SOLUTION: The area of a right triangle is 4 . The sum of the lengths of the two sides adjacent to the right angle of the triangle is 9 . What is the length of the hypotenuse of the triangle?      Log On


   

Question 702624: The area of a right triangle is 4 . The sum of the lengths of the two sides adjacent to the right angle of the triangle is 9 . What is the length of the hypotenuse of the triangle?
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Right triangle shown below, hypotenuse unlabeled, and legs x and y lengths.
Area was given as 4 [square units]:
%281%2F2%29%2Ax%2Ay=4

The sum of the legs' lengths given as 9 units:
x%2By=9

Now we have two equations and two unknowns, x and y.
From the area equation, we obtain x=8%2Fy, which we directly substitute into the length equation to obtain %288%2Fy%29%2By=9. Clearing the fraction yields
y%5E2-9%2Ay%2B8=0
.
...General solution to quadratic formula will give y = 1 or 8. This is just fine. Checking each using either equation from our system, gives x = 8 or 1.

ANSWER: The length of the legs are 1 and 8.
(please scroll down to see picture.)