Question 302686
Let's put down some formula first.
{{{P=2*(L+W)}}}
{{{A=L*W}}}
.
.
.
Now let's use the information we have,
"The perimeter of a rectangle is 20 meters"
{{{2*(L+W)=20}}}
1.{{{L+W=10}}}
"If the length is increased by four times the width, the sum is 19 meters"
2.{{{L+4W=19}}}
Now you have 2 equations with 2 unknowns. 
Use eq. 1,
{{{L+W=10}}}
{{{L=10-W}}}
Now substitute into eq. 2,
{{{L+4W=19}}}
{{{10-W+4W=19}}}
{{{3W=9}}}
{{{highlight_green( W=3) )}}}
Then from eq. 1,
{{{L=10-W}}}
{{{L=10-3}}}
{{{highlight_green( L=7)}}}
Then from those two,
{{{A=L*W=7(3)=highlight_green( 21)}}}