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 24 150 150 75 75 60

Answer 1

To find the area of the dilated triangle, we first need to calculate the area of the original triangle using the formula for the area of a triangle:

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

The original triangle has a base of 6 inches and a height of 4 inches. Plugging in these dimensions, we get:

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

Now, when the triangle is dilated by a scale factor of 2.5, both the base and height of the triangle are multiplied by this scale factor. Therefore, the new dimensions of the triangle 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 using these new dimensions:

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

So, the area of Mike's dilated triangle is \( \boxed{75} \) square inches.