```Question 293359

We basically have this triangle set up:

{{{drawing(500,500,-0.5,2,-0.5,3.2,
line(0,0,0,3),
line(0,3,2,0),
line(2,0,0,0),
locate(-0.2,1.5,x),
locate(1,-0.2,10),
locate(1,2,26)
)}}}

To find the unknown length, we need to use the Pythagorean Theorem.

Remember, the Pythagorean Theorem is {{{a^2+b^2=c^2}}} where "a" and "b" are the legs of a triangle and "c" is the hypotenuse.

Since the legs are {{{x}}} and {{{10}}} this means that {{{a=x}}} and {{{b=10}}}

Also, since the hypotenuse is {{{26}}}, this means that {{{c=26}}}.

{{{x^2+10^2=26^2}}} Plug in {{{a=x}}}, {{{b=10}}}, {{{c=26}}}

{{{x^2+100=26^2}}} Square {{{10}}} to get {{{100}}}.

{{{x^2+100=676}}} Square {{{26}}} to get {{{676}}}.

{{{x^2=676-100}}} Subtract {{{100}}} from both sides.

{{{x^2=576}}} Combine like terms.

{{{x=sqrt(576)}}} Take the square root of both sides. Note: only the positive square root is considered (since a negative length doesn't make sense).

{{{x=24}}} Take the square root of 576 to get 24.

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