SOLUTION: The legs of a right triangle are 4 cm and x cm. The hypotenuse is (2x-1) cm. What is x? I know the answer to this question is 3 but what I can't figure out is how that solution was

Question 813681: The legs of a right triangle are 4 cm and x cm. The hypotenuse is (2x-1) cm. What is x? I know the answer to this question is 3 but what I can't figure out is how that solution was achieved. I tried setting up the equation like but got the wrong answer. Can you help?
Found 3 solutions by Alan3354, ewatrrr, stanbon:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
The legs of a right triangle are 4 cm and x cm. The hypotenuse is (2x-1) cm. What is x? I know the answer to this question is 3 but what I can't figure out is how that solution was achieved. I tried setting up the equation like but got the wrong answer.
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It's

Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!

Hi,
The legs of a right triangle are 4 cm and x cm. The hypotenuse is (2x-1) cm.
| NOte: 16
3x^2 -4x - 15= 0

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=196 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 3, -1.66666666666667. Here's your graph:

Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
The legs of a right triangle are 4 cm and x cm. The hypotenuse is (2x-1) cm. What is x?
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Use Pythagoras:
leg^2 + leg^2 = hypotenuse^2
------
x^2 + 4^2 = (2x-1)^2
x^2 + 16 = 4x^2 - 4x + 1
----
3x^2 -4x -15 = 0
(x-3)(3x+5)= 0
x = 3 cm
2x-1 = 5 cm
================
Cheers,
Stan H.

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