In a right-angled triangle, the length of the medians from the vertices of acute angles are 7 cm and 4 6 cm. What is the length of the hypotenuse of the triangle (in cm)?

Answer: Option D

Solution

Answer: Option D

Solution:

$$\begin{array}{rl}& AD=7\text{ cm}\\ & CE=4\sqrt{6}\text{ cm}\\ & \text{Since, }4\left(A{D}^2+C{E}^2\right)=5A{C}^2\\ & 4\left({\left(7\right)}^2+{\left(4\sqrt{6}\right)}^2\right)=5A{C}^2\\ & 4\left(49+96\right)=5A{C}^2\\ & 4\left(145\right)=5A{C}^2\\ & A{C}^2=\frac{4\times 145}{5}\\ & AC=\sqrt{4\times 29}\\ & AC=2\sqrt{29}\text{ cm}\end{array}$$