The lengths of three medians of a triangle ar | vedclass

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(B) Let the medians be $m_1 = 9 \, cm$,$m_2 = 12 \, cm$,and $m_3 = 15 \, cm$. The area of a triangle with medians $m_1, m_2, m_3$ is given by the form

Vedclass · Accepted Answer

$72$

Vedclass · Answer

(B) Let the medians be $m_1 = 9 \, cm$,$m_2 = 12 \, cm$,and $m_3 = 15 \, cm$. The area of a triangle with medians $m_1, m_2, m_3$ is given by the formula: Area $= \frac{4}{3} \sqrt{s_m(s_m - m_1)(s_m - m_2)(s_m - m_3)}$,where $s_m = \frac{m_1 + m_2 + m_3}{2}$. Here,$s_m = \frac{9 + 12 + 15}{2} = \frac{36}{2} = 18 \, cm$. Area $= \frac{4}{3} \sqrt{18(18 - 9)(18 - 12)(18 - 15)}$ Area $= \frac{4}{3} \sqrt{18 	imes 9 	imes 6 	imes 3}$ Area $= \frac{4}{3} \sqrt{2916}$ Area $= \frac{4}{3} 	imes 54 = 72 \, cm^2$.

The lengths of three medians of a triangle are $9 \, cm$,$12 \, cm$,and $15 \, cm$. The area (in $cm^2$) of the triangle is

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