SOLUTION: i need to find the lengths of the three sides of the triangle given that the sides are x-5, 2x, and 2x+1. i know the answer is x=12, but i do not know how to get it using algebra

Algebra ->  Parallelograms -> SOLUTION: i need to find the lengths of the three sides of the triangle given that the sides are x-5, 2x, and 2x+1. i know the answer is x=12, but i do not know how to get it using algebra      Log On


   

Question 510706: i need to find the lengths of the three sides of the triangle given that the sides are x-5, 2x, and 2x+1. i know the answer is x=12, but i do not know how to get it using algebra
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
The problem, as stated, is not solvable!
If the triangle is a right triangle, or an equilateral triangle, you have to say so. Let's assume that it's a right triangle so we can use the Pythagorean theorem: c%5E2+=+a%5E2%2Bb%5E2
For any positive value of x, 2x+1 has to be the largest side and thus the hypotenuse (c) so...
%282x%2B1%29%5E2+=+%28x-5%29%5E2%2B%282x%29%5E2 Simplify.
4x%5E2%2B4x%2B1+=+x%5E2-10x%2B25%2B4x%5E2
4x%5E2%2B4x%2B1+=+5x%5E2-10x%2B25 Subtract 4x^2 from both sides.
4x%2B1+=+x%5E2-10x%2B25 Subtract 4x from both sides.
1+=+x%5E2-14x%2B25 Subtract 1 from both sides.
x%5E2-14x%2B24+=+0 Solve by factoring.
%28x-2%29%28x-12%29+=+0 Apply the zero product rule.
x-2+=+0 or x-2+=+0
x+=+2 or x+=+12 Discard x+=+2 as an invalid solution because x = 2 will give you a negative (x-5 = -3) side length.
Answer is x+=+12