SOLUTION: one leg of a right triangle measures three inches less than the other leg. find the length of both legs if the hypotenuse is 4 inches long

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Question 612626: one leg of a right triangle measures three inches less than the other leg. find the length of both legs if the hypotenuse is 4 inches long
Answer by nerdybill(7384) (Show Source):
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one leg of a right triangle measures three inches less than the other leg. find the length of both legs if the hypotenuse is 4 inches long
.
Let x = longer leg
then
x-3 = shorter leg
.
applying Pythagorean theorem:
x^2 + (x-3)^2 = 4^2
x^2 + (x-3)(x-3) = 16
x^2 + x^2-6x+9 = 16
2x^2-6x+9 = 16
2x^2-6x-7 = 0
applying the "quadratic formula" yields:
x = {3.9, -0.9}
throw out the negative solution (extraneous) leaving
x = 3.9 inches (longer leg)
.
shorter leg:
x-3 = 3.9-3 = .9 inches
.
answer: 3.9 inches and .9 inches
.
.
details of quadratic formula follows:

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=92 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 3.89791576165636, -0.89791576165636. Here's your graph: