Questions on Geometry: Pythagorean theorem answered by real tutors!

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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.: 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(2391) About Me  (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 ax^2+bx+c=0 (in our case 2x^2+3.6x+-3.01 = 0) has the following solutons:

x[12] = (b+-sqrt( b^2-4ac ))/2\a

For these solutions to exist, the discriminant b^2-4ac should not be a negative number.

First, we need to compute the discriminant b^2-4ac: b^2-4ac=(3.6)^2-4*2*-3.01=37.04.

Discriminant d=37.04 is greater than zero. That means that there are two solutions: x[12] = (-3.6+-sqrt( 37.04 ))/2\a.

x[1] = (-(3.6)+sqrt( 37.04 ))/2\2 = 0.621512405470294
x[2] = (-(3.6)-sqrt( 37.04 ))/2\2 = -2.42151240547029

Quadratic expression 2x^2+3.6x+-3.01 can be factored:
2x^2+3.6x+-3.01 = (x-0.621512405470294)*(x--2.42151240547029)
Again, the answer is: 0.621512405470294, -2.42151240547029. Here's your graph:
graph( 500, 500, -10, 10, -20, 20, 2*x^2+3.6*x+-3.01 )