Question

A rectangle on a coordinate plane has a length of 5 units and a width of 3 units. If the rectangle is dilated by a scale factor of 5, what is its new area?(1 point) square units

Answer 1

To find the area of the rectangle after dilation, we start with the original area.

1. Calculate the original area of the rectangle:
\[
\text{Original area} = \text{length} \times \text{width} = 5 \text{ units} \times 3 \text{ units} = 15 \text{ square units}
\]

2. A dilation by a scale factor of \(k\) multiplies both the length and width by that scale factor. In this case, the scale factor is 5.

- New length:
\[
\text{New length} = 5 \text{ units} \times 5 = 25 \text{ units}
\]

- New width:
\[
\text{New width} = 3 \text{ units} \times 5 = 15 \text{ units}
\]

3. Now, calculate the new area:
\[
\text{New area} = \text{New length} \times \text{New width} = 25 \text{ units} \times 15 \text{ units} = 375 \text{ square units}
\]

Therefore, the new area of the rectangle after dilation is \(375\) square units.