Chapter E, Problem 5.3EX

To determine

To Find:

The length of $T\overline{K}$ .

Answer to Problem 5.3EX

The length of $T\overline{K}$ is option (d) None of these.

Explanation of Solution

Given information:

M is the midpoint of hypotenuse $T\overline{K}$ of right $△TAK$ and $AM=13$ .

From the given information the triangle is assumed to be,

  $\begin{array}{l}\mathrm{Sin}{45}^{\circ }=\frac{Opposite}{Hypotenuse}=\frac{\frac{x}{2}}{13}\\ \Rightarrow \frac{1}{\sqrt{2}}=\frac{\frac{x}{2}}{13}\\ \Rightarrow \frac{13}{\sqrt{2}}=\frac{x}{2}\\ \Rightarrow \frac{13}{\sqrt{2}}\times 2=x\\ \Rightarrow \frac{13\times \sqrt{2}\times \sqrt{2}}{\sqrt{2}}=x\\ \Rightarrow 13\sqrt{2}=x\end{array}$

Therefore, the length of $T\overline{K}$ is option (d) None of these.