Question

The sides of a triangle are 11 cm, 15 cm and 16 cm. The altitude to the largest side is A. 30 √7 cm B. 15√7/2 cm C. 15√7/4 cm D. 30 cm

Answer 1

This is a high school level mathematics problem about finding the altitude to the largest side of a Heron's triangle. Using the given side lengths and the appropriate formula, we find that the answer is 15*sqrt(7)/2 cm (option B).

Step-by-step explanation:

The subject of this question is mathematics, specifically it revolves around the topic of geometry, in the area of triangle properties. The triangle given is a Heron's triangle given the lengths of its sides. The formula to find the altitude (h) to the largest side (b) of a triangle with sides of lengths a, b, and c is 2*sqrt(s*(s-a)*(s-b)*(s-c))/b, where s is the semi-perimeter of the triangle (s=(a+b+c)/2).

First calculate s=(11+15+16)/2=21. Substituting these values into the formula gives h = 2*sqrt(21*(21-11)*(21-15)*(21-16))/16 which simplifies to 15*sqrt(7)/2 cm. Therefore, the correct answer is option B.

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