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.

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)   (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)   (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)   (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.
...

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=64 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 6, -2. Here's your graph:

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.
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