SOLUTION: IN A RIGHT TRIANGLE, THE HYPOTENUSE IS 1 FOOT MORE THAN THE LONG LEG, WHILE THE SHORT LEG IS 11FT. LESS THAN HALF THE LONG LEG. YOUR GOAL IS TO FIND THE PERIMETER OF THIS TRIANGLE.

Question 952453: IN A RIGHT TRIANGLE, THE HYPOTENUSE IS 1 FOOT MORE THAN THE LONG LEG, WHILE THE SHORT LEG IS 11FT. LESS THAN HALF THE LONG LEG. YOUR GOAL IS TO FIND THE PERIMETER OF THIS TRIANGLE.
Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
b=long leg; a=short leg=(0.5b)-11ft; c=hypotenuse=b+1
Substitute for a and c, solve for b

Subtract 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=49 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 40, 12. Here's your graph:

b=40 or b=12 (long leg)
For b=40:
a=0.5b-11ft=0.5(40)-11 ft=9 ft (short leg)
c=b+1=40ft+1 ft=41 ft(hypotenuse)
For b=12
a=.5(12)-11 ft=6-11=-5ft does not work
ANSWER 1: The long leg is 40 feet.
ANSWER 2: The short leg is 9 feet.
ANSWER 3: The hypotenuse is 41 feet.
CHECK:

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