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# help

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The lengths of the sides of a traingle are 5,6 and 10 cm respectively. Find the square of the length of the median of the greatest side.

Jun 8, 2020

#1
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The lengths of the sides of a traingle are c=5, b=6 and a=10 cm respectively. Find the square of the length of the median of the greatest side.

Hello Guest!

$$m_a^2=\frac{1}{4}\cdot (2(b^2+c^2)-a^2)\\ m_a^2=\frac{1}{4}\cdot (2(36+25)-100)cm^2$$

$$m_a^2=5.5cm^2$$ !

Jun 8, 2020
edited by asinus  Jun 8, 2020
#2
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The lengths of the sides of a triangle are 5, 6 and 10 cm respectively.

Find the square of the length of the median of the greatest side. cos-rule:

$$\begin{array}{|lrcll|} \hline (1) & 6^2 &=& 5^2+10^2-2*5*10*\cos(A) \\ & 36 &=& 125-100\cos(A) \\ & 100\cos(A) &=& 125-36 \\ & 100\cos(A) &=& 89 \\ &\mathbf{ \cos(A) } &=& \mathbf{\dfrac{89}{100}} \\ \hline \end{array}$$

$$\begin{array}{|lrcll|} \hline (2) & x^2 &=& 5^2+5^2-2*5*5*\cos(A) \\ & x^2 &=& 50-50\cos(A) \\ & x^2 &=& 50-50*\dfrac{89}{100} \\ & x^2 &=& 50-\dfrac{89}{2} \\ & x^2 &=& 50-44.5 \\ &\mathbf{ x^2 } &=& \mathbf{5.5} \\ \hline \end{array}$$

The square of the length of the median of the greatest side is $$\mathbf{5.5}\ \text{cm}$$ Jun 8, 2020
edited by heureka  Jun 8, 2020
#3
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The lengths of the sides of a triangle are 5, 6, and 10 cm respectively. Find the square of the length of the median of the greatest side.

a = 5           b = 6        c = 10

(mc)2 = {[ sqrt( 2a2 + 2b2 - c2 )] / 2} = 5.5 cm2 Jun 8, 2020