Question 1134641


The rectangular floor of a closet is divided into two right triangles by drawing a diagonal. 
One leg of the right triangle is {{{10}}} feet less than twice  the other leg.




Let {{{w}}} be the width.  Then the length is {{{ (2w - 10)}}}.

Your equation to find "{{{w}}}" is

{{{w^2 + (2w-10)^2 = 25}}}


{{{5w^2 - 40 w + 100 = 625}}}.....simplify

{{{w^2 - 8 w + 20 = 125}}}

{{{w^2 - 8 w + 20 -125=0}}}

{{{w^2 - 8 w  -105=0}}}...factor

{{{(w - 15) (w + 7) = 0}}}

{{{w=15}}}
{{{w=-7}}}-> disregard negative solution



find the other leg = {{{2w-10}}}:

{{{2w-10=2*15-10=20}}}

 the​ closet's length is {{{20}}} ft and width is {{{15}}} ft