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?
A. 24
B. 75
C. 150
D. 60

Answer 1

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

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

For the original triangle, the height is 4 inches, and the base is 6 inches. Plugging these values into the formula gives:

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

Next, when we dilate the triangle by a scale factor of 2.5, the dimensions of the triangle will be multiplied by this scale factor. Specifically:

- The new height will be: \( 4 \times 2.5 = 10 \) inches
- The new base will be: \( 6 \times 2.5 = 15 \) inches

Now we can find the area of the dilated triangle using the same area formula:

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

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