To solve the problem, we need to find the area of both the original triangle and the dilated triangle.
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Find the area of the original triangle: The formula for the area of a triangle is given by: \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \] For the original triangle:
- Base = 10 cm
- Height = 15 cm
Plugging in these values: \[ \text{Area}_{\text{original}} = \frac{1}{2} \times 10 \times 15 = \frac{150}{2} = 75 \text{ cm}^2 \]
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Determine the dimensions of the dilated triangle: The scale factor for the dilation is \( \frac{4}{5} \). So, we need to multiply the base and height of the original triangle by this scale factor.
- New base = \( 10 \times \frac{4}{5} = 8 \) cm
- New height = \( 15 \times \frac{4}{5} = 12 \) cm
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Find the area of the dilated triangle: Using the same area formula for the dilated triangle: \[ \text{Area}_{\text{dilated}} = \frac{1}{2} \times 8 \times 12 = \frac{96}{2} = 48 \text{ cm}^2 \]
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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