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)
024
• 60
• 75
• 150

Answer 1

To find the area of the dilated triangle, we first need to calculate the area of the original triangle. The area \( A \) of a triangle can be found using the formula:

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

For the original triangle with a base of 6 inches and a height of 4 inches, the area is:

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

When the triangle is dilated by a scale factor of 2.5, the dimensions of the triangle are multiplied by 2.5. Therefore, 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 using the same area formula:

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

Thus, the area of Mike's dilated triangle is:

\[
\boxed{75} \text{ square inches}
\]