Question

question 9 of 28 what is the value of h in the diagram below? if necessary, round your answer to the nearest tenth of a unit. a. 9.1 b. 8.1 c. 3 d. 23

Explanation:

Step1: Use geometric mean theorem

In a right - triangle with an altitude drawn to the hypotenuse, we can use the geometric - mean theorem. The altitude \(h\) to the hypotenuse of a right - triangle divides the hypotenuse into two segments. The length of the altitude is the geometric mean between the lengths of the two segments of the hypotenuse. Here, the two segments of the hypotenuse are \(MP\) and \(PO\), and \(MP = 18 - 5=13\) and \(PO = 5\). The formula is \(h^{2}=MP\times PO\).

Step2: Calculate \(h\)

Substitute \(MP = 13\) and \(PO = 5\) into the formula \(h^{2}=MP\times PO\). So \(h^{2}=13\times5 = 65\). Then \(h=\sqrt{65}\approx 8.1\).

Answer:

B. 8.1