Question 168855
Call the length of the rod {{{x}}}
given:
The width is {{{x - 4}}}
The length is {{{x - 2}}}
The diagonal is {{{x}}}
{{{(x - 4)^2 + (x - 2)^2 = x^2}}}
{{{x^2 - 8x + 16 + x^2 - 4x + 4 = x^2}}}
{{{x^2 - 12x + 20 = 0}}}
{{{(x - 10)*(x - 2) = 0}}}
There are 2 solutions
{{{x = 2}}}
This is impossible because {{{x - 2 = 0}}} and {{{x - 4 = -2}}}
{{{x = 10}}} answer
{{{x - 2 = 8}}}
{{{x - 4 = 6}}}
The dimensions of the door are 6x8
check:
{{{(x - 4)^2 + (x - 2)^2 = x^2}}}
{{{(10 - 4)^2 + (10 - 2)^2 = 10^2}}}
{{{6^2 + 8^2 = 10^2}}}
{{{36 + 64 = 100}}}
{{{100 = 100}}}
OK