Answer
8 meters by 2.5 meters.
Work Step by Step
Step 1. Assume the length is $x$ and the width is $y$ meters.
Step 2. The perimeter is given by $2(x+y)=21$
Step 3. The area is given by $xy=20$ or $y=\frac{20}{x}$
Step 4. Using substitution, we have
$2(x+\frac{20}{x})=21$ or $2x^2+40=21x$ and $2x^2-21x+40=0$
Step 5. Factoring the equation, we have $(2x-5)(x-8)=0$, which gives $x=2.5$ or $8$ meters
Step 6. The corresponding widths are $y=8$ or $2.5$ meters.
Step 7. We can conclude the dimensions are 8 meters by 2.5 meters.
