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

Algebra ->  Triangles -> 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      Log On


   

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 +4x%5E2%2Bx%5E2=%282x-1%29%5E2 but got the wrong answer. Can you help?
Found 3 solutions by Alan3354, ewatrrr, stanbon:
Answer by Alan3354(69443) About Me  (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 +4x%5E2%2Bx%5E2=%282x-1%29%5E2 but got the wrong answer.
------------------
It's 4%5E2+%2B+x%5E2+=+%282x-1%29%5E2

Answer by ewatrrr(24785) About Me  (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.

+16++%2Bx%5E2=%282x-1%29%5E2=+4x%5E2+-4x+%2B+1+   | NOte:  16

    3x^2 -4x - 15= 0




 
Solved by pluggable solver: SOLVE quadratic equation with variable


Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-4x%2B-15+=+0) has the following solutons:

  

  x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

  

  For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

  

  First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-4%29%5E2-4%2A3%2A-15=196.

  

  Discriminant d=196 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--4%2B-sqrt%28+196+%29%29%2F2%5Ca.

  

    x%5B1%5D+=+%28-%28-4%29%2Bsqrt%28+196+%29%29%2F2%5C3+=+3

    x%5B2%5D+=+%28-%28-4%29-sqrt%28+196+%29%29%2F2%5C3+=+-1.66666666666667

    

    Quadratic expression 3x%5E2%2B-4x%2B-15 can be factored:

  3x%5E2%2B-4x%2B-15+=+3%28x-3%29%2A%28x--1.66666666666667%29

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

graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-4%2Ax%2B-15+%29

Answer by stanbon(75887) About Me  (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?
------
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.