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Three triangles are marked out of a bigger triangle at the three vertices such that each side of each of the smaller triangles is one-fourth as long as each corresponding side of the bigger triangle. The ratio of the area of the three small triangles taken together to that of the rest of the bigger triangle is:

Three triangles are marked out of a bigger triangle at the three vertices such that each side of each of the smaller triangles is one-fourth as long as each corresponding side of the bigger triangle. The ratio of the area of the three small triangles taken together to that of the rest of the bigger triangle is: Correct Answer 3 ∶ 13

Let the side of the bigger triangle be 12,

Three triangles are marked out of a bigger triangle at the three vertices such that each side of each of the smaller triangles is one-fourth as long as each corresponding side of the bigger triangle,

⇒ Side of the smaller triangle = 3

⇒ Ratio of area of bigger triangle to area of three smaller triangle = √3/4 × 122 ∶ 3 × √3/4 × 32 = 16 ∶ 3

∴ Ratio of the area of the three small triangles taken together to that of the rest of the bigger triangle = 3 ∶ 16 – 3 = 3 ∶ 13

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