Question 41011
Find the length x in each triangle.  Express your answer in simplified radical form.

long side is 12 
x is the straight side
8 is the bottom of the triangle

   {{{x^2 = 12^2 + 8^2}}}
        = 144 + 64
        = 208

Yip, but it's only wrong because the <i>long</i> side =shortest*middle.  so {{{12^2=x^2+8^2}}}
.:{{{144=x^2+64}}} minus 64 on both sides
{{{80=x^2}}} now square root both sides
{{{sqrt(80)=X}}}
simplify the radical
80-->2*2*2*2*5, or 16(5); and 16 is a perfect square of 4. therefore, 
{{{sqrt(80)}}}={{{sqrt(5*16)}}}={{{4sqrt(5)}}}  Otherwise, you would have been completely right.