SOLUTION: 5.) The lengths of the legs of a right triangle are consecutive even integers. The numerical value of the area is three times that of the longer leg. Find the lengths of the legs

Algebra ->  Circles -> SOLUTION: 5.) The lengths of the legs of a right triangle are consecutive even integers. The numerical value of the area is three times that of the longer leg. Find the lengths of the legs      Log On


   

Question 745003: 5.) The lengths of the legs of a right triangle are consecutive even integers. The numerical
value of the area is three times that of the longer leg. Find the lengths of the legs of the
triangle.
Answer by savvyhush23(50) About Me  (Show Source):
You can put this solution on YOUR website!
Let,
x - be the smaller leg
x+2 - (consecutive number)be the longer leg.
Area of triangle: A=%28x%29%28x%2B2%29%2F2
The numerical value of the area is three times that of the longer leg
A+=+3%28x%2B2%29
Equate both area:
%28x%29%28x%2B2%29%2F2=%28x%2B2%29
x%5E2-4x-12=0
Use quadratic formula:
x = 6 smaller leg
x + 2 = 8 larger leg