Given that the unshaded and shaded figures are similar:
1. scale factor = 36/25; x = 5.6 m
2. scale factor = 1/4; x = 2 ft
Areas of Similar Figures
- Where, a and b are the side length of two similar figures respectively, the ratio of their area would be, a²/b².
- The scale factor would be, a/b.
Thus:
Area of unshaded figure = 72 m²
Area of shaded figure = 50 m²
Side of unshaded figure = 8 m
Side of shaded figure = x m
Therefore:
Scale factor = 72/50 = 36/25
Solve for x:
8/x = 36/25
x = (8×25)/36
x = 5.6 m
Area of unshaded figure = 16 ft²
Area of shaded figure = 64 ft²
Side of unshaded figure = x ft
Side of shaded figure = 8 ft
Therefore:
Scale factor = 16/64 = 1/4
Solve for x:
x/8 = 1/4
x = (1×8)/4
x = 2 ft
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