SOLUTION: Two sides of a right triangle are 5 and 10 inches more than the first side. Using the Pythagorean rule, (a^2 + b^2 = c^2), where "c" is the longest side find all three lengths

Algebra ->  Pythagorean-theorem -> SOLUTION: Two sides of a right triangle are 5 and 10 inches more than the first side. Using the Pythagorean rule, (a^2 + b^2 = c^2), where "c" is the longest side find all three lengths      Log On


   

Question 956142: Two sides of a right triangle are 5 and 10 inches more than the first side. Using the Pythagorean rule, (a^2 + b^2 = c^2), where "c" is the longest side find all three lengths
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
a=short side; b=middle side=a+5in; c=long side=hypotenuse=a+10in
a%5E2%2Bb%5E2=c%5E2
a%5E2%2B%28a%2B5in%29%5E2=%28a%2B10in%29%5E2
a%5E2%2Ba%5E2%2B10a%2B25=a%5E2%2B20a%2B100
a%5E2-10a-75=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aa%5E2%2Bba%2Bc=0 (in our case 1a%5E2%2B-10a%2B-75+=+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=%28-10%29%5E2-4%2A1%2A-75=400.

Discriminant d=400 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--10%2B-sqrt%28+400+%29%29%2F2%5Ca.

a%5B1%5D+=+%28-%28-10%29%2Bsqrt%28+400+%29%29%2F2%5C1+=+15
a%5B2%5D+=+%28-%28-10%29-sqrt%28+400+%29%29%2F2%5C1+=+-5

Quadratic expression 1a%5E2%2B-10a%2B-75 can be factored:
1a%5E2%2B-10a%2B-75+=+1%28a-15%29%2A%28a--5%29
Again, the answer is: 15, -5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-10%2Ax%2B-75+%29

a=15 ANSWER 1: The shortest side is 15 inches.
b=a+5in=15in+5in=20in ANSWER 2: The middle side is 20 inches long.
c=a+10in=15in+10in=25in ANSWER 3: The hypotenuse is 25 inches.
CHECK:
a%5E2%2Bb%5E2=c%5E2
15%5E2in%5E2%2B20%5E2in%5E2=25%5E2in%5E2
225in%5E2%2B400in%5E2=625in%5E2
625in%5E2=625in%5E2