SOLUTION: The hypotenuse of a right triangle is 70 inches long. One leg is 2 inch(es) longer than the other. Find the lengths of the legs of the triangle. Round your answers to the nearest t

Algebra ->  Pythagorean-theorem -> SOLUTION: The hypotenuse of a right triangle is 70 inches long. One leg is 2 inch(es) longer than the other. Find the lengths of the legs of the triangle. Round your answers to the nearest t      Log On


   

Question 952478: The hypotenuse of a right triangle is 70 inches long. One leg is 2 inch(es) longer than the other. Find the lengths of the legs of the triangle. Round your answers to the nearest tenth of an inch.
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
a=short leg; b=long leg=a+2in; c=hypotenuse=70in
a%5E2%2Bb%5E2=c%5E2
a%5E2%2B%28a%2B2in%29%5E2=%2870in%29%5E2
a%5E2%2Ba%5E2%2B4a%2B4=4900in%5E2
(((2a^2+4a-4896in^2=0}}}
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aa%5E2%2Bba%2Bc=0 (in our case 2a%5E2%2B4a%2B-4896+=+0) has the following solutons:

a%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%284%29%5E2-4%2A2%2A-4896=39184.

Discriminant d=39184 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+39184+%29%29%2F2%5Ca.

a%5B1%5D+=+%28-%284%29%2Bsqrt%28+39184+%29%29%2F2%5C2+=+48.4873721266345
a%5B2%5D+=+%28-%284%29-sqrt%28+39184+%29%29%2F2%5C2+=+-50.4873721266345

Quadratic expression 2a%5E2%2B4a%2B-4896 can be factored:
2a%5E2%2B4a%2B-4896+=+2%28a-48.4873721266345%29%2A%28a--50.4873721266345%29
Again, the answer is: 48.4873721266345, -50.4873721266345. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B4%2Ax%2B-4896+%29

a=48.5in ANSWER 1:The short leg is 48.5 in.
b=a+2in=50.5in ANSWER 2: The long leg is 50.5 in.