Question

The lengths of sides of a triangle are 30 m, 26 m and 28 m. What is the length of the altitude drawn on the longest
side from opposite vertex?

Answer:
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Answer 1

$\underline{\textsf{Given:}}$

$\textsf{The lengths of sides of the triangle are 30m, 26m, 28m}$

$\underline{\textsf{To find:}}$

$\textsf{Length of the altitude drawn on the longest side}$

$\underline{\textsf{Solution:}}$

$\mathsf{First we find out, the area of the given triangle}$

$\textsf{We apply Heron's formula to find the area}$

$\mathsf{s=\dfrac{a+b+c}{2}=\dfrac{30+26+28}{2}=\dfrac{84}{2}=42}$

$\mathsf{Area\;of\;the\;trianlge=\sqrt{s(s-a)(s-b)(s-c)}}$

$\mathsf{Area\;of\;the\;trianlge=\sqrt{42(42-30)(42-26)(42-28)}}$

$\mathsf{Area\;of\;the\;trianlge=\sqrt{42{\times}12{\times}16{\times}14}}$

$\mathsf{Area\;of\;the\;trianlge=\sqrt{6{\times}7{\times}6{\times}2{\times}4^2{\times}2{\times}7}}$

$\mathsf{Area\;of\;the\;trianlge=\sqrt{2^2{\times}4^2{\times}6^2{\times}7^2}}$

$\mathsf{Area\;of\;the\;trianlge=2{\times}4{\times}6{\times}7}}$

$\mathsf{Area\;of\;the\;trianlge=336\;square\;units}$

$\textsf{Let h be the length of the altitude drawn on the 30 cm side}$

$\implies\mathsf{\dfrac{1}{2}{\times}30{\times}h=336}$

$\implies\mathsf{15{\times}h=336}$

$\implies\mathsf{h=\dfrac{336}{15}}$

$\implies\mathsf{h=22.4\;cm}$

$\underline{\textsf{Answer:}}$

$\textsf{The length of the required altitude is 22.4 cm}$

Find more:

Sides of the triangle are 13cm, 14cm and 15 cm, find the length of thesmallest altitude of the triangle.

https://brainly.in/question/17401153

Answer 2

Answer:

your answer is 22 mate hope this helps