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

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) (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:

Now we solve for x. First we simplify. (Be sure to use FOIL or the pattern to square the x+17 and the 3x+4.)

Since this is a quadratic equation we want one side to be zero. Subtracting the entire left side from each side we get:

This will factor, but not easily. So you may prefer to use the Quadratic Formula instead.

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
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