SOLUTION: The hypotenuse of a right triangle is 4 cm longer than the shortest side and 2 cm longer than the remaining side. Find the dimensions of the triangle.

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Question 446283: The hypotenuse of a right triangle is 4 cm longer than the shortest side and 2 cm longer than the remaining side. Find the dimensions of the triangle.
Found 3 solutions by stanbon, jorel1380, chriswen:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The hypotenuse of a right triangle is 4 cm longer than the shortest side and 2 cm longer than the remaining side. Find the dimensions of the triangle.
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Let shortest side be "x".
The hypotenuse = "x+4"
And 3rd side is "x-2".
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Equation:
x^2 + (x-2)^2 = (x+4)^2
x^2 + x^2-4x+4 = x^2+4x+16
x^2-8x-12 = 0
----
(x-6)(x-2) = 0
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x = 6 or x = 2
====================
Cheers,
Stan H.
===============

Answer by jorel1380(3719) About Me  (Show Source):
You can put this solution on YOUR website!
x2+(x+2)2=(x+4)2
x2+x2+4x+4=x2+8x+16
2x2+4x+4=x2+8x+16
x2-4x-12=0
(x-6)(x+2)=0
x=6 or -2
Throwing out the negative answer, we get x=6,x+2=8, and x+4=10..

Answer by chriswen(106) About Me  (Show Source):
You can put this solution on YOUR website!
Let x cm be the shortest side.
Let x+2 cm be the other leg.
Let x+4 cm be the hypotenuse of the triangle.
...
x%5E2%2B%28x%2B2%29%5E2=%28x%2B4%29%5E2
x%5E2%2Bx%5E2%2B4x%2B4=x%5E2%2B8x%2B16
2x%5E2-x%5E2%2B4x-8x%2B4-16=0
x%5E2-4x-12=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-4x%2B-12+=+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%2A1%2A-12=64.

Discriminant d=64 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--4%2B-sqrt%28+64+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-4%29%2Bsqrt%28+64+%29%29%2F2%5C1+=+6
x%5B2%5D+=+%28-%28-4%29-sqrt%28+64+%29%29%2F2%5C1+=+-2

Quadratic expression 1x%5E2%2B-4x%2B-12 can be factored:
1x%5E2%2B-4x%2B-12+=+1%28x-6%29%2A%28x--2%29
Again, the answer is: 6, -2. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-4%2Ax%2B-12+%29

The answer has to be positive so
x=6
x+2=8
x+4=10
Therefore, the dimensions of the triangle is 6cm by 8cm by 10cm.