Question

question 5 of 10
what is the value of x in the figure below? in this diagram, \\( \triangle a b d \sim \triangle c a d \\).

a. \\( \frac { 9 } { 14 } \\)
b. 14
c. 45
d. \\( \sqrt { 70 } \\)
e. \\( \sqrt { 45 } \\)
f. \\( \sqrt { 126 } \\)

Explanation:

Step1: Use the geometric mean theorem (altitude-on-hypotenuse theorem)

For two similar right - angled triangles \(\triangle ABD\sim\triangle CAD\), we have the formula \(x^{2}=BD\times DC\).

Step2: Substitute the values of \(BD\) and \(DC\)

Given \(BD = 5\) and \(DC=9\), then \(x^{2}=5\times9\).

Step3: Calculate \(x\)

\(x^{2}=45\), so \(x = \sqrt{45}\) (since \(x>0\) as it represents a length).

Answer:

E. \(\sqrt{45}\)