Answer
$\frac{4x^{2}}{25x^{2}+30x+9}$ square meters
Work Step by Step
Step 1: Length $L$= $\frac{2x}{5x+3}$ meters
Step 2: Area of square =$L \times L$= $\frac{2x}{5x+3} \times \frac{2x}{5x+3}$
Step 3: $\frac{2x}{5x+3} \times \frac{2x}{5x+3} =\frac{2x\times2x}{(5x+3)(5x+3)}$
Step 4: $\frac{4x^{2}}{(5x+3)^{2}}$
Step 5: $\frac{4x^{2}}{(5x)^{2}+2(5x)(3)+(3)^{2}}$
Step 6: $\frac{4x^{2}}{25x^{2}+30x+9}$
Step 6: Therefore, the answer is $\frac{4x^{2}}{25x^{2}+30x+9}$ square meters