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.
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!
\(m_a^2=\frac{1}{4}\cdot (2(b^2+c^2)-a^2)\\ m_a^2=\frac{1}{4}\cdot (2(36+25)-100)cm^2\)
\(m_a^2=5.5cm^2\)
!
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 \(\mathbf{5.5}\ \text{cm}\)