The areas of two similar triangles are 169 sq.cm and 121 sq.cm. If the longest side of larger triangle is 26 cm, then the length of the longest side of the other triangle is ____.

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. Setting up the proportion 169 / 121 = (26 / x)^2, we take the square root of both sides to get 13 / 11 = 26 / x. Cross-multiplying yields 13x = 286. Dividing by 13 gives the length of the longest side of the smaller triangle as 22 cm.

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