SOLUTION: The hypotenuse of a right triangle is 30 feet. One leg is 12 less than twice the other leg. Find the dimension of the triangle. So I have 30ft as the hypotenuse, then 2x-12 for

Algebra ->  Triangles -> SOLUTION: The hypotenuse of a right triangle is 30 feet. One leg is 12 less than twice the other leg. Find the dimension of the triangle. So I have 30ft as the hypotenuse, then 2x-12 for       Log On


   

Question 843173: The hypotenuse of a right triangle is 30 feet. One leg is 12 less than twice the other leg. Find the dimension of the triangle.
So I have 30ft as the hypotenuse, then 2x-12 for the one leg, and x for the third. Where do I go from here? It has been a year since I took geometry.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

The hypotenuse of a right triangle is 30 feet. 

One leg is 12 less than twice the other leg highlight_green%28x%29

Good Work on the Set Up of x and (2x-12) for the legs

Applying the Pythagorean Theorem:

 x^2 + (2x-12)^2 = 30^2

 x^2 + (2x-12)(2x-12) = 30^2

 x^2 + 4x^2 + 48x + 144 = 900

   5x^2 - 48x - 756 = 0     |Form:  ax^2 + bx + c = 0

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

x+=+%2848%2B-+sqrt%28+17424%29%29%2F%2810%29+

x+=+%2848%2B-+132%29%2F%2810%29+    |Tossing out negative solution for unit measure

     x = 18ft, one leg.  The other is 24ft    2%2A18+-+12

CHECKING our answer***

 18^2 + 24^2 = 324 + 576 = 900 

Wish You the Best in your Studies.