Calculate Dimensions: Finding Lengths of a 750 m² Plot from a 20×25 m² Similar Plot

Let's solve the problem by using the relationship between similar figures.

The area of the first plot is $20 \times 25 = 500 \, \text{m}^2$. The area of the second plot is given as $750 \, \text{m}^2$.

We use the property of similar figures where the ratio of their areas is the square of the ratio of their corresponding lengths.

Let the ratio of similarity (scale factor) be $k$, so:

$\left(\frac{500}{750}\right) = k^2$

Simplified, this becomes:

$k^2 = \frac{2}{3}$

Taking the square root of both sides:

$k = \sqrt{\frac{2}{3}}$

To find the dimensions of the second plot, multiply the dimensions of the first plot by $k^{-1}$ (as the second plot is larger, we use reciprocal since direct $k$ reduces dimensions):

The first plot dimensions are 20 m and 25 m. Applying the scale factor:

• Length 1 of second plot = $20 \cdot \left(\sqrt{\frac{3}{2}}\right) = 20\sqrt{\frac{3}{2}} = 10\sqrt{6}$
• Length 2 of second plot = $25 \cdot \left(\sqrt{\frac{3}{2}}\right) = 25\sqrt{\frac{3}{2}} = \frac{25\sqrt{6}}{2}$

Hence, the dimensions of the second plot are $10\sqrt{6} \times \frac{25\sqrt{6}}{2}$.

This matches option 3.

Therefore, the calculated lengths of the second plot of land are $10\sqrt{6} \, \text{m}$ and $\frac{25\sqrt{6}}{2} \, \text{m}$.