SOLUTION: A drawing of a teepee has the shape of a right triangle with one leg 8 meters longer than the other, The hypotenuse is 8 meters less than twice the length of the shorter leg? What

Algebra ->  Pythagorean-theorem -> SOLUTION: A drawing of a teepee has the shape of a right triangle with one leg 8 meters longer than the other, The hypotenuse is 8 meters less than twice the length of the shorter leg? What       Log On


   

Question 1005015: A drawing of a teepee has the shape of a right triangle with one leg 8 meters longer than the other, The hypotenuse is 8 meters less than twice the length of the shorter leg? What are the steps with the solution?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Step 1: Define a variable
x= length of the shorter leg, in meters.

Step 2: Express other measurements based on the variable defined above.
x%2B8= length of the shorter leg, in meters.
2x-8= length of the hypotenuse/

Step 3: Apply the Pythagorean theorem
%282x-8%29%5E2=x%5E2%2B%28x%2B8%29%5E2

Step 4: Work on the above equation (simplify and solve)
%282x-8%29%5E2=x%5E2%2B%28x%2B8%29%5E2
%282x%29%5E2%2B2%282x%29%28-8%29%2B8%5E2=x%5E2%2Bx%5E2%2B2%28x%29%288%29%2B8%5E2
4x%5E2-32x%2B8%5E2=x%5E2%2Bx%5E2%2B16x%2B8%5E2
4x%5E2-32x=2x%5E2%2B16x
4x%5E2-32x-2x%5E2-16x=0
2x%5E2-48x=0
2x%28x-24%29=0--->x=24 is the only solution that makes sense, because
x=0 does not make sense.

Step 5: Find the other lengths
x%2B8=24%2B8=32 and 2x-8=2%2A24%2A8=48-8=40 .

Step 6: Answer in words, with units if that is what is expected.
The shorter leg measures highlight%2824meters%29 .
The longer leg measures highlight%2832meters%29 .
The hypotenuse measures highlight%2840meters%29 .