Ratio of the areas

Geometry Level 2

The first triangle has 3 edges: a,b,c. The edges of the second triangle are 2a,2b, 2c.So what is the ratio of the area between the first and the second triangle?

16 8 4 2

Sky Lawson by Sky lawson , 17, Vietnam

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3 solutions

Het Patel
Aug 19, 2018

correct your question. make it " ratio of second to first triangle" .

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Thank you very much.

Sky lawson - 2 years, 9 months ago
Edwin Gray
Sep 2, 2018

Let's make it more complicated, but rigorous. By Hero's formula A 1 = sqrt(s(s-a)(s-b)(s-c)), where s = (a+b+c)/2. A 2 = sqrt(2s(2s-2a)(2s-2b)(2s-2c))= sqrt(16 A_1)^2) =4 A_1. Ed Gray

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Sky Lawson
Aug 19, 2018

Because the edges of 2 triangles have the ratio of 2, so the 2 triangles are congruent triangles. In congruent triangles, the area ratio is equal to edges ratio square.

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