SOLUTION: The length of one leg of a right triangle is 2 cm less than three times the length of other leg. The area of the triangle is 48 cm^2. Find the length of each leg. Please show work!

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: The length of one leg of a right triangle is 2 cm less than three times the length of other leg. The area of the triangle is 48 cm^2. Find the length of each leg. Please show work!      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 291783: The length of one leg of a right triangle is 2 cm less than three times the length of other leg. The area of the triangle is 48 cm^2. Find the length of each leg. Please show work! thank u
Answer by eggsarecool(46) About Me  (Show Source):
You can put this solution on YOUR website!
Ok so lets call one leg x
The other leg is three times the length 3x and 2 cm less so 3x-2.
The Area of a triangle is A=%281%2F2%29%2Ab%2Ah
For a right Triangle the base is one leg and the height is the other leg.
We also know that the Area is 48. A=48
So Multiply by 2 to cancel the 1%2F2
96=3x%5E2-2x Subtract 96 from both sides.
3x%5E2-3x-96=0 Factor out the 3.
3%28x%5E2-x-32%29=0 Use the qudratic formula to solve/
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-1x%2B-32+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-1%29%5E2-4%2A1%2A-32=129.

Discriminant d=129 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--1%2B-sqrt%28+129+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+129+%29%29%2F2%5C1+=+6.17890834580027
x%5B2%5D+=+%28-%28-1%29-sqrt%28+129+%29%29%2F2%5C1+=+-5.17890834580027

Quadratic expression 1x%5E2%2B-1x%2B-32 can be factored:
1x%5E2%2B-1x%2B-32+=+1%28x-6.17890834580027%29%2A%28x--5.17890834580027%29
Again, the answer is: 6.17890834580027, -5.17890834580027. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-1%2Ax%2B-32+%29


And since you cannot have a negative length in a triangle, 6.17890834580027 is the length of the leg we called x. To find the length of the other leg multiply by 3 and then subtract 2 to get the length of the other leg.
3%2A6.17890834580027-2=16.53672503740081
So the length of the other leg is 16.53672503740081