A triangle has a base of 8 cm and a height of 3 cm. The triangle is dilated by a scale factor of 3. Calculate and compare the areas of the dilated triangle and the original triangle. (1 point) Responses The original triangle has an area of 12 cm2 and the dilated triangle has an area of 36 cm2 ; therefore, the dilated triangle has an area 3 times the size of the original triangle. The original triangle has an area of 12 cm squared and the dilated triangle has an area of 36 cm squared ; therefore, the dilated triangle has an area 3 times the size of the original triangle. The original triangle has an area of 24 cm2 and the dilated triangle has an area of 36 cm2 ; therefore, the dilated triangle has an area 1.5 times the size of the original triangle. The original triangle has an area of 24 cm squared and the dilated triangle has an area of 36 cm squared ; therefore, the dilated triangle has an area 1.5 times the size of the original triangle. The original triangle has an area of 12 cm2 and the dilated triangle has an area of 108 cm2 ; therefore, the dilated triangle has an area 9 times the size of the original triangle. The original triangle has an area of 12 cm squared and the dilated triangle has an area of 108 cm squared ; therefore, the dilated triangle has an area 9 times the size of the original triangle. The original triangle has an area of 24 cm2 and the dilated triangle has an area of 108 cm2 ; therefore, the dilated triangle has an area 4.5 times the size of the original triangle.

Answer 1

To find the area of the original triangle, you can use the formula for the area of a triangle:

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

For the original triangle:

\[ \text{Area} = \frac{1}{2} \times 8 , \text{cm} \times 3 , \text{cm} = \frac{24}{2} = 12 , \text{cm}^2 \]

Next, when the triangle is dilated by a scale factor of 3, the new base and height will be:

\[ \text{New base} = 3 \times 8 , \text{cm} = 24 , \text{cm} \] \[ \text{New height} = 3 \times 3 , \text{cm} = 9 , \text{cm} \]

Now we calculate the area of the dilated triangle:

\[ \text{Dilated Area} = \frac{1}{2} \times 24 , \text{cm} \times 9 , \text{cm} = \frac{216}{2} = 108 , \text{cm}^2 \]

Now comparing the areas:

• Original triangle area: \(12 , \text{cm}^2\)
• Dilated triangle area: \(108 , \text{cm}^2\)

To find out how many times larger the dilated triangle's area is compared to the original triangle's area:

\[ \text{Comparison} = \frac{108 , \text{cm}^2}{12 , \text{cm}^2} = 9 \]

So the dilated triangle has an area 9 times the size of the original triangle.

The correct response is:

The original triangle has an area of 12 cm² and the dilated triangle has an area of 108 cm²; therefore, the dilated triangle has an area 9 times the size of the original triangle.