SOLUTION: The hypotenuse of a right triangle is 2.5 units long. The longer leg is 1.8 units longer than the shorter leg. Find the lengths of the sides of the triangle.

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Question 147605: The hypotenuse of a right triangle is 2.5 units long. The longer leg is 1.8 units longer than the shorter leg. Find the lengths of the sides of the triangle.
Answer by edjones(8007)   (Show Source): You can put this solution on YOUR website!
c=2.5
a=b+1.8
a^2+b^2=c^2
(b+1.8)^2+b^2=(2.5)^2
b^2+3.6b+3.24+b^2=6.25
2b^2+3.6b-3.01=0
b=.621512
a=2.42151
c=2.5
.
Ed
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
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=37.04 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 0.621512405470294, -2.42151240547029. Here's your graph:
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