Question

question 7 of 10
what is the value of h in the figure below? in this diagram, \\( \triangle bad \sim \triangle cbd \\).

a. 16
b. \\( \frac { 16 } { 9 } \\)
c. \\( \frac { 25 } { 9 } \\)
d. 12
e. 400
f. \\( \sqrt { 225 } \\)

Explanation:

Step1: Use the geometric mean theorem

For similar right - angled triangles \(\triangle BAD\sim\triangle CBD\), the length of the altitude \(h\) to the hypotenuse of a right - triangle is the geometric mean of the lengths of the two segments of the hypotenuse. Let the two segments of the hypotenuse be \(x\) and \(y\). Here, \(x = 25 - 16=9\) and \(y = 16\). The formula is \(h=\sqrt{xy}\).

Step2: Calculate the value of \(h\)

Substitute \(x = 9\) and \(y = 16\) into the formula \(h=\sqrt{xy}\). So \(h=\sqrt{9\times16}\). Since \(\sqrt{9\times16}=\sqrt{9}\times\sqrt{16}\), and \(\sqrt{9} = 3\), \(\sqrt{16}=4\), then \(h = 3\times4=12\).

Answer:

D. 12