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?M

(1 point)
Responses

150
150

60
60

75
75

24

Answer 1

To find the area of Mike's dilated triangle, we can follow these steps:

1. **Calculate the area of the original triangle:**
The area \( A \) of a triangle is given by the formula:
\[
A = \frac{1}{2} \times \text{base} \times \text{height}
\]
For the original triangle:
- Base = 6 inches
- Height = 4 inches

So the area of the original triangle is:
\[
A = \frac{1}{2} \times 6 \times 4 = \frac{1}{2} \times 24 = 12 \text{ square inches}
\]

2. **Use the scale factor to find the area of the dilated triangle:**
The area of a shape scales by the square of the scale factor when dilated. In this case, the scale factor is 2.5. Therefore, the area of the dilated triangle can be calculated as:
\[
\text{Area of dilated triangle} = \text{Area of original triangle} \times \text{(scale factor)}^2
\]
\[
= 12 \times (2.5)^2
\]
\[
= 12 \times 6.25 = 75 \text{ square inches}
\]

Therefore, the area of Mike's dilated triangle is **75 square inches**.