Question 319085
First name the variables.
{{{L}}}-length of the rectangular garden
{{{W}}}-width of the rectangular garden
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Now translate the words to equations,
"length should be 10 more than the width"
1.{{{L=10+W}}}
"total area enclosed will be 180 ft^2"
What's the area of a rectangle???
In terms of its length and width, the area is,
{{{A=L*W}}}
2.{{{L*W=180}}}
Now you have two independent equations with two unknowns, you can solve for each.
Substitute eq. 1 into eq. 2,
{{{(10+W)W=180}}}
{{{10W+W^2=180}}}
{{{W^2+10W-180=0}}}
Use the quadratic formula,
{{{W= (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
{{{W= (-10 +- sqrt( 10^2-4*1*(-180) ))/(2*1) }}} 
{{{W= (-10 +- sqrt( 100+720 ))/(2) }}} 
Only the positive result makes sense in this case.
{{{W= (-10 + sqrt(820 ))/(2) }}}
{{{W= (-10 + 2*sqrt( 205 ))/(2) }}} 
{{{highlight(W= -5 + sqrt( 205 )) }}} ft
Then from above,
{{{L=10+W}}}
{{{highlight(L=5+sqrt(205))}}} ft