SOLUTION: The hypotenuse of a right triangle is 2.5 units long. The longer leg is 1.5 units longer than the shorter leg. Find the lengths of the sides of the triangle. Please help me to

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Question 166813: The hypotenuse of a right triangle is 2.5 units long. The longer leg is 1.5 units longer than the shorter leg. Find the lengths of the sides of the triangle.
Please help me to get to the answer.
Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website!
The hypotenuse of a right triangle is 2.5 units long. The longer leg is 1.5 units longer than the shorter leg. Find the lengths of the sides of the triangle.
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Let x = length of shorter leg
then from "leg is 1.5 units longer than the shorter leg"
x+1.5 = length of longer leg
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Applying Pythagorean theorem:
x^2 + (x+1.5)^2 = 2.5^2
x^2 + x^2+3x+2.25 = 6.25
2x^2+3x+2.25 = 6.25
2x^2+3x-4 = 0
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Since we can't factor, use the quadratic equation. Doing so will produce:
x = {0.851, -2.351}
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We can toss out the negative solution leaving us with the sides as:
0.851 units and 2.351 units
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The following is the details of the quadratic:

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=41 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 0.850781059358212, -2.35078105935821. Here's your graph: