SOLUTION: the length of one leg of a right triangle is 17cm more than that of the other leg. The length of the hypotenue is 4 vm more than triple that of the shorter leg. Find the lenghts of

Algebra ->  Pythagorean-theorem -> SOLUTION: the length of one leg of a right triangle is 17cm more than that of the other leg. The length of the hypotenue is 4 vm more than triple that of the shorter leg. Find the lenghts of      Log On


   

Question 697554: the length of one leg of a right triangle is 17cm more than that of the other leg. The length of the hypotenue is 4 vm more than triple that of the shorter leg. Find the lenghts of each of the three sides
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = the shorter leg. Then the longer leg would be (x + 17) and the hypotenuse would be (3x + 4). In order for this to be a right triangle these sides must fit the Pythagorean equation:
%28x%29%5E2+%2B+%28x%2B17%29%5E2+=+%283x%2B4%29%5E2
Now we solve for x. First we simplify. (Be sure to use FOIL or the %28a%2Bb%29%5E2+=+a%5E2%2B2ab%2Bb%5E2 pattern to square the x+17 and the 3x+4.)
x%5E2+%2B+x%5E2%2B2%2Ax%2A17%2B17%5E2+=+%283x%29%5E2+%2B+2%283x%29%284%29+%2B4%5E2
x%5E2+%2B+x%5E2%2B34x%2B289+=+9x%5E2+%2B+24x+%2B+16
2x%5E2%2B34x%2B289+=+9x%5E2+%2B+24x+%2B+16
Since this is a quadratic equation we want one side to be zero. Subtracting the entire left side from each side we get:
0+=+7x%5E2-10x-273
This will factor, but not easily. So you may prefer to use the Quadratic Formula instead.
0+=+%287x%2B39%29%28x-7%29
From the Zero Product Property:
7x + 39 = 0 or x - 7 = 0
Solving these we get:
x = -39/7 or x = 7
We will reject the first solution not because it is a fraction but because it is negative. x is the length of the shorter leg and we cannot have negative lengths.

So the shorter leg is 7 cm.
The longer leg would be x + 17 = 7 + 17 = 24 cm
And the hypotenuse would be 3x + 4 = 3(7) + 4 = 21 + 4 = 25 cm