SOLUTION: one leg of a triangle is 7 ft longer than other leg. The length of the hypothenuse is 13ft. Find the lengths of the other two sides. How would I set this up? I know its a² + b²

Algebra ->  Pythagorean-theorem -> SOLUTION: one leg of a triangle is 7 ft longer than other leg. The length of the hypothenuse is 13ft. Find the lengths of the other two sides. How would I set this up? I know its a² + b²      Log On


   

Question 428650: one leg of a triangle is 7 ft longer than other leg. The length of the hypothenuse is 13ft. Find the lengths of the other two sides.
How would I set this up? I know its a² + b² = c² but I don't know which is which or how to go about setting it up to solve.
Found 2 solutions by ewatrrr, Gogonati:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi

one leg of a triangle is 7 ft longer than other leg

Let x and (x+7)represent th elengths of the two legs respectively

 a² + b² = c² 

 x^2 + (x+7)^2 = 13^2

 2x^2 + 14x -120 = 0

 x^2 + 7x - 60 = 0

(x + 12)(x-5) = 0

(x + 12)=0  x = 12  |tossing out negative solution for length

 (x-5) = 0

  x = 5, the other side is 12  (5+7)



 CHECKING our Answer***

 25 + 144 = 169 = 13^2

Answer by Gogonati(855) About Me  (Show Source):
You can put this solution on YOUR website!
Let x ft the length of one leg. Then the other leg will be: x+7 ft. Since the hypotenuse is 13 ft, we write the Pythagorean theorem:
x%5E2%2B%28x%2B7%29%5E2=13%5E2
x%5E2%2Bx%5E2%2B14x%2B7%5E2=13%5E2, Set the equation to zero.
2x%5E2%2B14x-120=0, divide both sides by 2
x%5E2%2B7x-60=0, factor the equation.
(x-5)(x+12)=0 => x-5=0 => x=5 and x+12=0 => x=-12 Since the length is always positive, the root -12 is rejected.
Answer: The short leg is 5 ft and the long one is 5+7=12 ft.