Question 164851
To understand this problem first draw a representation of a right triangle.  Label one leg x and the other leg x-2.
Given:  the hypotenuse is 4 cm. more than the shorter leg so:
label the hypotenuse x-2+4 or x+2
Now use the Pythagorean Theorem to find the value of x
{{{(x)^2+(x-2)^2=(x+2)^2}}}
or
{{{x^2+(x-2)(x-2)=(x+2)(x+2)}}}
Order of operations says we have to multiply where possible so use the FOIL method.
{{{x^2+x^2-2x-2x+4=x^2+2x+2x+4}}}
combine like terms:
{{{2x^2-4x+4=x^2+4x+4}}}
Move everything to the same side.
Subtract x^2 from both sides and you get:
{{{x^2-4x+4=4x+4}}}
Subtract 4x from both sides and you get:
x^2-8x+4=4
Subtract 4 from both sides and you get:
x^2-8x=0
Factor out an x and you get:
x(x-8)=0
This statement is true when x=0 or (x-8)=0
x-8=0
add 8 to both sides and you get 
x=8

x=0;x=8  However, because we are dealing with a length of a triangle x cannot=0
Therefore x=8 is the only answer to this problem.

Check your work!
your sides are 8;8-2;8-2+4 or 8;6;10
we know that {{{8^2+6^2=10^2}}}
or 
64+46=100
or 
100=100 and therefore the answer checks out to be true.

Remember that you must always try to find a unit label for every answer.  In this case it is centimeters so your final answer is 6 cm; 8 cm; and 10 cm
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