SOLUTION: one leg of a right is 2 millimeters shorter than the longer leg and the hypotenuse is 2 millimeters longer than the longer leg. find the lengths of the sides of the triangle. find

Question 949117: one leg of a right is 2 millimeters shorter than the longer leg and the hypotenuse is 2 millimeters longer than the longer leg. find the lengths of the sides of the triangle. find the lengths of the sides of the triangle
Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
a=shorter leg; b=longer leg=a+2; c=hypotenuse=a+4
Substitute for b and c

Subtract a^2 from each side.
Subtract 8a from each side.
Subtract 16 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=64 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 6, -2. Here's your graph:

So the solution we want is 6
The length of the shorter leg is 6 mm.
b=a+2 mm=6 mm+2 mm=8 mm The length of the longer leg is 8 mm.
c=a+4 mm=6 mm+4 mm=10 mm The length of the hypotenuse is 10 mm, so we have a 3-4-5 right triangle.

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