Questions: The dimensions of the original rectangle are 3.5 by 2.5 m Select all the possible dimensions of the scaled copy. 1.75 meters and 1.25 meters 7 meters and 5 meters 7 meters and 6 meters 10 meters and 2.5 meters 10.5 meters and 7.5 meters

Solution Steps

To determine if the given dimensions are possible scaled copies of the original rectangle, we need to check if the ratio of the dimensions of the scaled copies is the same as the ratio of the original rectangle. The ratio of the original rectangle is 3.5/2.5. We will compare this ratio with the ratios of the given dimensions.

The dimensions of the original rectangle are 3.5 meters by 2.5 meters. To find the ratio, we divide the width by the height: \[ \text{Original Ratio} = \frac{3.5}{2.5} = 1.4 \]

We need to check if the ratio of each given dimension pair matches the original ratio of 1.4. We will calculate the ratio for each pair and compare it to 1.4.

1. For dimensions \(1.75\) meters and \(1.25\) meters: \[ \frac{1.75}{1.25} = 1.4 \] This matches the original ratio.

2. For dimensions \(7\) meters and \(5\) meters: \[ \frac{7}{5} = 1.4 \] This matches the original ratio.

3. For dimensions \(7\) meters and \(6\) meters: \[ \frac{7}{6} \approx 1.1667 \] This does not match the original ratio.

4. For dimensions \(10\) meters and \(2.5\) meters: \[ \frac{10}{2.5} = 4 \] This does not match the original ratio.

5. For dimensions \(10.5\) meters and \(7.5\) meters: \[ \frac{10.5}{7.5} = 1.4 \] This matches the original ratio.

Final Answer