SOLUTION: 4)The flower garden has the shape of a right triangle. 34 ft of a perennial border forms the hypotenuse of the triangle, and one leg is 14 ft longer than the other leg. Find the le

Algebra ->  Pythagorean-theorem -> SOLUTION: 4)The flower garden has the shape of a right triangle. 34 ft of a perennial border forms the hypotenuse of the triangle, and one leg is 14 ft longer than the other leg. Find the le      Log On


   

Question 129827: 4)The flower garden has the shape of a right triangle. 34 ft of a perennial border forms the hypotenuse of the triangle, and one leg is 14 ft longer than the other leg. Find the lengths of the legs.
What are the lengths of the legs? ______ft
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let a=x (ie let the first leg be represented by the unknown variable)

Since one leg is 14 ft longer than the other leg, this means b=x%2B14

a%5E2%2Bb%5E2=c%5E2 Start with pythagorean's theorem

x%5E2%2B%28x%2B14%29%5E2=34%5E2 Plug in a=x, b=x%2B14, and c=34


x%5E2%2B%28x%2B14%29%5E2=1156 Square 34 to get 1156

x%5E2%2Bx%5E2%2B28x%2B196=1156 Foil x%2B14 to get x%5E2%2B28x%2B196

x%5E2%2Bx%5E2%2B28x%2B196-1156=0 Subtract 1156 from both sides

2x%5E2%2B28x-960=0 Combine like terms

2x%5E2%2B28x-960=0 Start with the given equation

2%28x%2B30%29%28x-16%29=0 Factor the left side


Now set each factor equal to zero:
x%2B30=0 or x-16=0

x=-30 or x=16 Now solve for x in each case


So our answer is
x=-30 or x=16

However, since a negative length doesn't make any sense, our only solution is

x=16


So the first leg is 16 ft


Now simply add 14 to 16 to get the length of the other leg

16%2B14=30


So the second leg is 30 ft