Three heights are drawn in the triangle, the largest and the smallest of which are equal to 15 and 12.

| August 19, 2021 | education

Three heights are drawn in the triangle, the largest and the smallest of which are equal to 15 and 12. Find the larger side of the triangular if the smaller of its sides is 20.

Let a triangle ABC be given, the smaller of its sides BC = 20. Three heights are drawn in the triangle, the largest of which is AH = 15, and the smaller BK = 12. To find the length of the larger side AC of triangle ABC, to which the lower height is dropped, we use the property of heights in a triangle. It is known that the lengths of the heights are inversely proportional to the lengths of the corresponding sides to which they are drawn, that is, AH: BK = AC: BC. Substitute the values ​​of the quantities and make the calculations: 15: 12 = AC: 20; AC = (15: 12) ∙ 20 = 25 (unit segments).
Answer: 20 unit segments is the length of the larger side of the ABC triangle.



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