Question

Use the image to answer the question.

A triangle with unequal sides with the base labelled 6 and height labelled 4.

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

75
75

60
60

150
150

24

Answer 1

To find the area of Mike's dilated triangle, we first need to calculate the area of the original triangle.

The formula for the area of a triangle is:

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

For the original triangle:
- Base = 6 inches
- Height = 4 inches

Plugging in these values:

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

Now, when Mike dilates the triangle by a scale factor of 2.5, the dimensions of the triangle will increase by this scale factor.

The new base and height will be:

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

Now we can calculate the area of the dilated triangle:

\[
\text{Dilated Area} = \frac{1}{2} \times \text{new base} \times \text{new height} = \frac{1}{2} \times 15 \times 10
\]

Calculating this:

\[
\text{Dilated Area} = \frac{1}{2} \times 150 = 75 \text{ square inches}
\]

Thus, the area of Mike’s dilated triangle is 75 square inches.

The correct response is:

75