# SOLUTION: The hypotenuse of a right triangle is 8 ft. longer than one leg and 4 ft. longer than the other leg. What are the dimensions of this triangle? Show the equation you used to solve t

Algebra ->  -> SOLUTION: The hypotenuse of a right triangle is 8 ft. longer than one leg and 4 ft. longer than the other leg. What are the dimensions of this triangle? Show the equation you used to solve t      Log On

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 Click here to see ALL problems on Triangles Question 128479: The hypotenuse of a right triangle is 8 ft. longer than one leg and 4 ft. longer than the other leg. What are the dimensions of this triangle? Show the equation you used to solve this and then your answer. Answer by Earlsdon(6294)   (Show Source): You can put this solution on YOUR website!Let c = the hypotenuse and a and b the other two legs. From the problem description, you can write: and Rewrite these in terms of a and b to get: and Now you can use the Pythagorean theorem to find c, the hypotenuse: Substitute the two equations above for a and b: Simplify. Combine like-terms. Subtract from both sides. Solve this quadratic by factoring: , so then... or Discard the first solution as c must be greater than 8 or else you have one leg of the triangle equal to zero! So, the hypotenuse is 20 and the other two legs are a=12 and b = 16. Check: Substitute c = 20, a = 12, and b = 16. OK!