Question 333575
When you are dealing with a right triangle and you are trying to find lenght of the sides, you will most likely end up using the pythagorean theorem which states:   {{{c^2=a^2+b^2}}} where c is the side opposite the right angle, and is called the hypotenuse.
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Given in your problem:  c=5, a=x and b=x+1
so by the pythagorean theorem of a right triangle:  {{{5^2 = x^2 + (x+1)^2}}}
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{{{25=x^2 + (x^2+2x+1)}}}    (expanding the squared term)
{{{25=2x^2+2x+1}}}    (combining terms)
{{{0=2x^2+2x-24}}}   (putting the quadratic equation in standard form}}}

{{{0=x^2+x-12}}}     (divide the whole thing by 2, to simplify the equation)
0=(x+4)*(x-3)   (factor the expression on the right)
x=-4, x=3, since we are dealing with lengths, the negative value x= -4 is extraneous and can be trown out
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so, one side is a=x=3 and the other is b=x+1=4
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what you have is a special type of right triangle where the sides are in a ratio  3:4:5