Question 1104857
<br>
The length, width, and diagonal of the rectangle form a right triangle.<br>
Let the length be x and the width x-8; then the Pythagorean Theorem tells us<br>
{{{x^2 + (x-8)^2 = (6*sqrt(2))^2}}}
{{{x^2+x^2-16x+64 = 72}}}
{{{2x^2-16x-8 = 0}}}
{{{x^2-8x-4 = 0}}}
{{{x = (8+-sqrt(64-4(1)(-4)))/2 = (8+-sqrt(80))/2 = (8+-sqrt(5)*4)/2 = 4+-sqrt(5)*2}}}<br>
The length of the rectangle is {{{x = 4+2*sqrt(5)}}}; the width is {{{x-8 = -4+2*sqrt(5)}}}.<br>