Chapter 8.1, Problem 49HP

To determine

Toexplain:

Identification of error in the given statement “aiden and tia are finding the value of $x$ ”

Answer to Problem 49HP

Aiden and tia neither of them is correct as the value of $x\approx 5.7$ .

Explanation of Solution

Given information:

  Aiden    Tia

  $\begin{array}{l}\frac{4}{x}=\frac{x}{7}\\ x\approx 5.3\end{array}$$\begin{array}{l}\frac{4}{x}=\frac{x}{10}\\ x\approx 6.3\end{array}$

  

The altitude drawn to the hypotenuse of a right triangle separates the hypotenuse into two segments. The length of this altitude is the geometric mean between the lengths of these two segments.

So, geometric mean altitude theorem shows that,

  $\begin{array}{l}x=\sqrt{8\left(4\right)}\\ =\sqrt{32}\\ =4\sqrt{2}\\ \approx 5.7\end{array}$

Therefore, neither of them is correct.