SOLUTION: The hypotenuse of a right triangle measures 20cm. The sum of the lengths of the other 2 sides is 28cm. Find the lengths of these two sides. x(squared) + (28 - x)(squared)

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Question 185852: The hypotenuse of a right triangle measures 20cm. The sum of the lengths of the other 2 sides is 28cm. Find the lengths of these two sides.
x(squared) + (28 - x)(squared) = 20(squared)
Let x be the length of one side. Therefore the length of the other side is 28 – x.
Found 2 solutions by solver91311, edjones:
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!



You have your equation already:





Standard form:



Divide by 2:



Factor and solve. Either root can be x and the other will be 28 - x.

John
Answer by edjones(8007)   (Show Source): You can put this solution on YOUR website!
c=20, a+b=28
a^2+b^2=c^2
x^2+(28-x)^2=20^2
x^2+x^2-56x+784=400
2x^2-56x+384=0
2(x^2-28x+192)=0
x^2-28x+192=0
x=12, x=16 these are the two sides.
.
Ed
.
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=16 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 16, 12. Here's your graph:
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