Question

Mike draws a triangle and dilates it by a scale factor of 2.5. If the triangle’s original dimensions are 4 inches high and 6 inches along its base, what is the area in square inches of Mike’s dilated triangle?

(1 point)
Responses

24
24

75
75

60
60

150

Answer 1

To find the area of a triangle, use the formula:

\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]

First, we calculate the area of the original triangle using its dimensions:

\[
\text{Area}_{\text{original}} = \frac{1}{2} \times 6 \, \text{inches} \times 4 \, \text{inches} = \frac{1}{2} \times 24 \, \text{square inches} = 12 \, \text{square inches}
\]

Next, when the triangle is dilated by a scale factor of 2.5, the dimensions (height and base) are multiplied by this scale factor. The new height and base measurements are:

\[
\text{New height} = 2.5 \times 4 \, \text{inches} = 10 \, \text{inches}
\]
\[
\text{New base} = 2.5 \times 6 \, \text{inches} = 15 \, \text{inches}
\]

Now we can calculate the area of the dilated triangle:

\[
\text{Area}_{\text{dilated}} = \frac{1}{2} \times 15 \, \text{inches} \times 10 \, \text{inches} = \frac{1}{2} \times 150 \, \text{square inches} = 75 \, \text{square inches}
\]

Thus, the area of Mike's dilated triangle is:

\[
\boxed{75}
\]