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The University of Texas at El Paso
Christopher W.
Algebra
6 months, 3 weeks ago
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A pair of corresponding sides of two similar triangles are 4 and 9. Find the ratio of the triangles' areas.
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Let the areas of two similar triangles be A1, A2 and their corresponding sides be S1, S2 respectively.
∴ `"A"_1/"A"_2 = 144/49` ...(i)[Given]
∴ by the theorem of areas of similar triangles,
∴ `"A"_1/"A"_2 = "S"_1^2/"S"_2^2`
∴ `144/49 = "S"_1^2/"S"_2^2` ...[From (i)]
∴ by taking square root of both sides,
∴ `"S"_1/"S"_2 = 12/7`
∴ The ratio of the corresponding sides of the given triangles is 12: 7.