SOLUTION: The hypotenuse of a right triangle is 7 less than three times the shortest leg. The longest leg is two less than the hypotenuse. Detemine the lengths of all three sides. There a

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: The hypotenuse of a right triangle is 7 less than three times the shortest leg. The longest leg is two less than the hypotenuse. Detemine the lengths of all three sides. There a      Log On


   

Question 149780: The hypotenuse of a right triangle is 7 less than three times the shortest leg. The longest leg is two less than the hypotenuse. Detemine the lengths of all three sides. There are two sets of answers, state both of them.
Answer by kmcruz09(38) About Me  (Show Source):
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The hypotenuse of a right triangle is 7 less than three times the shortest leg. The longest leg is two less than the hypotenuse. Detemine the lengths of all three sides. There are two sets of answers, state both of them.
let x = shortest leg
then 3x-7 = hypotenuse
then 3x-9 = longest leg
x%5E2+%2B+%283x-9%29%5E2+=+%283x-7%29%5E2
x%5E2+%2B+9x%5E2+-54x+%2B81+=+9x%5E2-42x%2B49
x%5E2+-+54x+%2B+81+=+-42x+%2B+49
x%5E2+-+12x+%2B+32+=+0
%28x-8%29%28x-4%29=0
x=8
x=4
Triangle 1 : 8, 17, 15
Triangle 2: 4, 5, 3
in the case of Triangle 2, 3x-9 is equal to 3. It doesn't satisfy the conditions given in the problem that 3x-9 must be the longest leg. Therefore, the sides of Triangle 1 should be considered as the only correct answer.