Question 50272
width = w
length = l
Perimeter:
{{{2l + 2w = 26}}}
{{{2l = 26 - 2w}}}
{{{l = 13 - w}}}
Area:
{{{lw = 40}}}
Plug:
{{{(13 - w)w = 40}}}
{{{13w - w^2 = 40}}}
{{{0 = w^2 - 13w + 40}}}
{{{0 = w^2 - 5w - 8w + 40}}}
{{{0 = w(w - 5) - 8(w - 5)}}}
{{{0 = (w - 8)(w - 5)}}}
w = 8 or w = 5
plug:
{{{lw = 40}}}
{{{8l = 40}}}
{{{l = 5}}}
so: either 8 x 5  or  5 x 8
Since the length is longer than the width:
length = 8 meters
width = 5 meters