SOLUTION: A right triangle has a height that is 6 inches longer than its shorter side. The hypotenuse of the triangle is 7 inches longer than the shorter side. How long is the hypotenuse of

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Question 955361: A right triangle has a height that is 6 inches longer than its shorter side. The hypotenuse of the triangle is 7 inches longer than the shorter side. How long is the hypotenuse of the triangle?
Answer by macston(5194)   (Show Source): You can put this solution on YOUR website!
a=short side; b=a+6in; c=a+7in
Substitute for b and c.

Subtract (a^2+14a+49) from each side.
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=56 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 4.74165738677394, -2.74165738677394. Here's your graph:

a=4.74in
b=a+6=10.74in
c=a+7=11.74in ANSWER: The hypotenuse is 11.74 inches.
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