Question 1009519: These kinds of questions easily confuse me...an explanation would be so helpful, thank you in advance.
The length of the hypotenuse of a right triangle is 3 less than 4 times the length of the shortest leg. The length of the other leg is 3 more than 3 times the length of the shortest leg. What are the lengths of all 3 sides?
Answer by fractalier(6550)   (Show Source):
You can put this solution on YOUR website! If we cal the length of the shortest leg x, then
the hypotenuse is 4x - 3.
The other leg is 3x + 3.
Then we apply the Pythagorean Theorem, a^2 + b^2 = c^2 and get
x^2 + (3x+3)^2 = (4x-3)^2
x^2 + 9x^2 + 18x + 9 = 16x^2 - 24x + 9
Now we collect like terms and get
6x^2 - 42x = 0
6x(x - 7) = 0
so that x = 0 or x = 7
But x cannot be zero, so x = 7 and the three sides are
7, 24 and 25.
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