To raise a scale copy of the rectangle and assess the dimensions, we will identify the "skill" (likely referring to the scaling factor or ratio used for resizing), and then express the dimensions of the new shape in simplest form.
Given dimensions:
- Left triangle: 45 (base) and \( \frac{75}{4} \) (height)
- Right triangle: 36 (base) and 15 (height)
Step 1: Determine the Scaling Factor
To calculate the scaling factor, we generally need to know a specific target size or use a common scale ratio. Since the scaling factor isn't provided, let's assume a hypothetical case. Suppose we want to scale both triangles by the ratio of their bases.
The bases are:
- Left triangle: 45
- Right triangle: 36
The scaling factor \( k \) can be determined from the bases: \[ k = \frac{\text{Base of Right Triangle}}{\text{Base of Left Triangle}} = \frac{36}{45} = \frac{4}{5} \]
Step 2: Scaling the Dimensions
We apply the scaling factor \( k = \frac{4}{5} \) to both triangles’ dimensions.
For Left Triangle
-
Base: \[ \text{Scaled Base} = 45 \times \frac{4}{5} = 36 \]
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Height: \[ \text{Scaled Height} = \left( \frac{75}{4} \right) \times \frac{4}{5} = \frac{75}{5} = 15 \]
For Right Triangle
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Base: \[ \text{Scaled Base} = 36 \times \frac{4}{5} = \frac{144}{5} = 28.8 \]
-
Height: \[ \text{Scaled Height} = 15 \times \frac{4}{5} = 12 \]
Summary of Scaled Dimensions:
-
Left Triangle (scaled):
- Base: 36
- Height: 15
-
Right Triangle (scaled):
- Base: 28.8 (or \( \frac{144}{5} \))
- Height: 12
Conclusion
The process followed illustrates how to scale both triangles based on a hypothetical scaling ratio derived from their existing base dimensions. You can apply different scaling factors if other criteria are provided.
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