Question

Marisol draws a triangle with a 4-inch base and 6-inch height. She dilates the triangle by a scale factor of 1.5. Compare the areas of the dilated triangle and the original triangle. Use a decimal response if necessary. (1 point) The area of the dilated triangle is times the area of the original triangle

Answer 1

To find the areas of the original triangle and the dilated triangle, we can use the formula for the area of a triangle:

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

**Step 1: Calculate the area of the original triangle.**

Given:
- Base = 4 inches
- Height = 6 inches

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

**Step 2: Calculate the dimensions of the dilated triangle.**

The scale factor is 1.5, so we multiply the base and the height of the original triangle by this factor.

- Dilated base = \(4 \times 1.5 = 6\) inches
- Dilated height = \(6 \times 1.5 = 9\) inches

**Step 3: Calculate the area of the dilated triangle.**

\[
\text{Area}_{\text{dilated}} = \frac{1}{2} \times 6 \times 9 = \frac{1}{2} \times 54 = 27 \text{ square inches}
\]

**Step 4: Compare the areas of the dilated triangle and the original triangle.**

To find how many times the area of the original triangle fits into the area of the dilated triangle:

\[
\frac{\text{Area}_{\text{dilated}}}{\text{Area}_{\text{original}}} = \frac{27}{12} = 2.25
\]

Thus, the area of the dilated triangle is **2.25 times** the area of the original triangle.

The final answer is:

**2.25**