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.
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 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 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 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.%0D%0AThe original triangle has an area of 24 cm squared and the dilated triangle has an area of 108 cm squared ; therefore, the dilated triangle has an area 4.5 times the size of the original triangle.
The original triangle has a base of 8 cm and a height of 3 cm, so its area is given by the formula: A = 1/2 * base * height. Substituting the given values, we have: A = 1/2 * 8 cm * 3 cm = 12 cm².
The dilated triangle has a scale factor of 3, which means that all its sides (including the base) are multiplied by 3. Therefore, the new base of the dilated triangle is 3 * 8 cm = 24 cm and the new height is 3 * 3 cm = 9 cm. Using the same formula, the area of the dilated triangle is: A = 1/2 * 24 cm * 9 cm = 108 cm².
Comparing the areas, we can see that the dilated triangle has an area 9 times the size of the original triangle. So, the correct option 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.