Two triangular sails have exactly the same shape, and each side of the smaller sail is 3/5 of the matching side of the larger sail. What is the ratio of their areas, smaller to larger?

Question 32

EasyOriginal question

Two triangular sails have exactly the same shape, and each side of the smaller sail is $\frac{3}{5}$ of the matching side of the larger sail. What is the ratio of their areas, smaller to larger?

9 : 25

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3 : 5

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\sqrt{3} : \sqrt{5}

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27 : 125

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CorrectNot quiteAnswer A

Correct answer: A

The sails are similar triangles with side ratio $3 : 5$ .
Areas of similar triangles are in the ratio of the squares of their sides: $3^2 : 5^2 = 9 : 25$ .

Worth noting

$3 : 5$ is the ratio of the sides, not the areas. $27 : 125$ would be the ratio of volumes of similar solids.

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