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Find the ratio of thel length
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[tex] (\dfrac{L_1}{L_2})^3 = \dfrac{V_1}{V_2} [/tex]
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Substitute the value of the given volume
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[tex] (\dfrac{L_1}{L_2})^3 = (\dfrac{512}{3375} )[/tex]
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Cube Root both sides
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[tex] (\dfrac{L_1}{L_2}) = \sqrt[3]{\dfrac{512}{3375} } [/tex]
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Ratio of the length of the 2 similar rectangle
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[tex] (\dfrac{L_1}{L_2}) = \dfrac{8}{15} [/tex]
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Find the area of the larger figure
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[tex] (\dfrac{L_1}{L_2})^2 = \dfrac{A_1}{A_2} [/tex]
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Substitute the known number to the ratio
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[tex](\dfrac{8}{15})^2 = \dfrac{128}{A_2}[/tex]
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Evaluate the left hand side
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[tex]\dfrac{64}{225} = \dfrac{128}{A_2}[/tex]
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Cross multiply and Solve
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[tex]64 \times A_2=128 \times 225[/tex]
[tex]A_2 = 28800 \div 64[/tex]
[tex]A_2 = 450 \ mm^2[/tex]
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Answer: Area = 450 mm²
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