To solve the problem, we need to find the area of both the original triangle and the dilated triangle.
-
Find the area of the original triangle: The formula for the area of a triangle is given by:
For the original triangle:- Base = 10 cm
- Height = 15 cm
Plugging in these values:
-
Determine the dimensions of the dilated triangle: The scale factor for the dilation is
. So, we need to multiply the base and height of the original triangle by this scale factor.- New base =
cm - New height =
cm
- New base =
-
Find the area of the dilated triangle: Using the same area formula for the dilated triangle:
-
Calculate the difference between the areas: We find the difference in areas by subtracting the area of the dilated triangle from the area of the original triangle: \[ \text{Difference} = \text{Area}{\text{original}} - \text{Area}{\text{dilated}} = 75 - 48 = 27 \text{ cm}^2 \]
Thus, the area of the original triangle is greater than the area of the dilated triangle by:
B. 27 cm²