We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website.
Please click on "Accept cookies" if you agree to the setting of cookies. Cookies that do not require consent remain unaffected by this, see
cookie policy and privacy policy.
DECLINE COOKIES

Medians are drawn from point A and point B in this right triangle to divide segments BC and AC in half, respectively. The lengths of the medians are 6 and 2\sqrt{11} units, respectively. How many units are in the length of segment AB.

Guest Mar 28, 2018

#1**+2 **

**Medians are drawn from point A and point B in this right triangle to divide segments BC and AC in half, respectively. The lengths of the medians are 6 and \( 2\sqrt{11}\) units, respectively.**

**How many units are in the length of segment AB.**

\(\text{Let $c = AB $} \\ \text{Let $a = BC $} \\ \text{Let $b = CA $} \)

\(\begin{array}{|lrcll|} \hline (1) & \left(\dfrac{1}{2}a \right)^2 + b^2 &=& 6^2 \\ (2) & a^2 + \left(\dfrac{1}{2}b \right)^2 &=& (2\sqrt{11})^2 \\ \hline (1) + (2): & \left(\dfrac{1}{2}a \right)^2 + b^2 + a^2 + \left(\dfrac{1}{2}b \right)^2 &=& 6^2 + (2\sqrt{11})^2 \\ & \dfrac{5}{4}a^2 + \dfrac{5}{4}b^2 &=& 36+44 \\ & \dfrac{5}{4}(a^2 + b^2) &=& 80 \quad & | \quad a^2+b^2=c^2 \\ & \dfrac{5}{4}c^2 &=& 80 \\ & c^2 &=& \dfrac{4\cdot 80}{5} \\ & c^2 &=& 4\cdot 16 \\ & c &=& 2\cdot 4 \\ & \mathbf{c} & \mathbf{=} & \mathbf{8} \\ \hline \end{array}\)

The length of segment AB = **8**

heureka Mar 28, 2018