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

60
60

75

Answer 1

To find the area of the dilated triangle, we first calculate the area of the original triangle and then apply the scale factor for the area.

1. **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

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

2. **Apply the scale factor to find the area of the dilated triangle:**
When a shape is dilated by a scale factor of \( k \), the area of the new shape is scaled by \( k^2 \). Here, the scale factor \( k = 2.5 \).

\[
k^2 = (2.5)^2 = 6.25
\]

Thus, the area of the dilated triangle is:
\[
\text{Dilated Area} = \text{Original Area} \times k^2 = 12 \times 6.25 = 75 \text{ square inches}
\]

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