Question

The median of a rightangled triangle whose lengths are drawn from the vertices of the acute angles are 5 and $\sqrt{40}$. The value of the hypotenuse is

• A. 10
• B. $2\sqrt{40}$
• C. $\sqrt{13}$
• D. $2\sqrt{13}$

Answer 1

The correct option is D $2\sqrt{13}$

Since,

$BD=DC=x$

$AE=BE=y$

Now, ${EC}^2={EB}^2+{BC}^2$

$\Rightarrow 25={\left(2x\right)}^2+y^2⟶\left(i\right)$

& ${AD}^2={AB}^2+{BD}^2$

$\Rightarrow 40={\left(2y\right)}^2+x^2⟶\left(ii\right)$

From $\left(i\right)$ & $\left(ii\right)$

$25=4(40-{4y}^2)+y^2$

$\Rightarrow {15y}^2=135\Rightarrow y=3$ & $x=2$

Now,

$AC=\sqrt{4(x^2+y^2)}$

$=2\sqrt{13}$ units

Hence, this is the answer.