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!

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) (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
For a right Triangle the base is one leg and the height is the other leg.
We also know that the Area is 48.
So Multiply by 2 to cancel the
Subtract 96 from both sides.
Factor out the 3.
Use the qudratic formula to solve/

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=129 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 6.17890834580027, -5.17890834580027. Here's your graph:

And since you cannot have a negative length in a triangle, 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.

So the length of the other leg is
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