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

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) (Show Source): You can put this solution on YOUR website!
Let (ie let the first leg be represented by the unknown variable)

Since one leg is 14 ft longer than the other leg, this means

Start with pythagorean's theorem

Plug in , , and

Square 34 to get 1156

Foil to get

Subtract 1156 from both sides

Combine like terms

Start with the given equation

Factor the left side

Now set each factor equal to zero:
or

or Now solve for x in each case

So our answer is
or

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

So the first leg is 16 ft

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

So the second leg is 30 ft
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