Question

question 2 of 10
what is the value of m in the figure below? in this diagram, (\triangle abdsim\triangle bcd).
a
14
d
5
b
m
c
a. (sqrt{650})
b. (sqrt{95})
c. (sqrt{323})
d. (sqrt{48})
e. (sqrt{221})
f. (sqrt{70})

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle ABD\sim\triangle BCD\), the ratios of corresponding sides are equal. That is \(\frac{AD}{BD}=\frac{BD}{CD}\). Here \(AD = 14\), \(CD=5\), and \(BD = n\).

Step2: Set up the proportion

Substituting the values into the proportion \(\frac{14}{n}=\frac{n}{5}\). Cross - multiply to get \(n^{2}=14\times5\).

Step3: Solve for \(n\)

\(n^{2}=70\), then \(n = \sqrt{70}\) (we take the positive value since \(n\) represents the length of a side in a geometric figure).

Answer:

F. \(\sqrt{70}\)