SOLUTION: Ski Jump. The base of a ski ramp forms a right triangle. One leg of the triangle is 2 meters longer than the others. If the hypotenuse is 10 meters, then what are the lengths of

Algebra ->  Algebra  -> Customizable Word Problem Solvers  -> Geometry -> SOLUTION: Ski Jump. The base of a ski ramp forms a right triangle. One leg of the triangle is 2 meters longer than the others. If the hypotenuse is 10 meters, then what are the lengths of      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

   

Question 156174This question is from textbook College Algebra
: Ski Jump. The base of a ski ramp forms a right triangle. One leg of the triangle is 2 meters longer than the others. If the hypotenuse is 10 meters, then what are the lengths of the legs?This question is from textbook College Algebra

Answer by jojo14344(1512) About Me  (Show Source):
You can put this solution on YOUR website!
let x=adjacent
x%2B2=opposite, 2 meters longer
10m=hypotenuse
by Pyth theorem:
hyp%5E2=adj%5E2%2Bopp%5E2
10%5E2=x%5E2%2B%28x%2B2%29%5E2
100=x%5E2%2Bx%5E2%2B4x%2B4
2x%5E2%2B4x%2B4-100=0 ---> 2x%5E2%2B4x-96=0, Divide the whole eqn by 2 to reduce
cross%282%29x%5E2%2Fcross%282%29%2Bcross%284%292x%2Fcross%282%29-cross%2896%2948%2Fcross%282%29=0
x%5E2%2B2x-48=0
BY QUADRATIC, a=1, b=2, & c=-48
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x=%28-2%2B-sqrt%282%5E2-4%2A1%2A-48%29%29%2F%282%2A1%29
x=%28-2%2B-sqrt%284%2B192%29%29%2F2=%28-2%2B-sqrt%28196%29%29%2F2
x=%28-2%2B-14%29%2F2, 2 values:
x=%28-2%2B14%29%2F2=12%2F2=6 ---------------------> TO BE USED
x=%28-2-14%29%2F2=-16%2F2=-8 -------------------> DON'T USE (-)
So, adjacent=x=6meters
opposite=x%2B2=6%2B2=8meters
In doubt? go back Pyth Theorem:
10%5E2=6%5E2%2B8%5E2
100=36%2B64
100m=100m
Thank you,
Jojo