Question

question 7 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. 20
b. 5
c. \\( \frac { 45 } { 4 } \\)
d. \\( \sqrt { 10 } \\)
e. \\( \frac { 20 } { 15 } \\)
f. \\( \sqrt { 300 } \\)

Explanation:

Step1: Recall Similar Triangles Property

For similar triangles \(\triangle ABD \sim \triangle CAD\), the corresponding sides are proportional. So, \(\frac{CA}{CB}=\frac{CD}{CA}\).

Step2: Identify Known Values

We know \(CA = 15\), \(CB = 20\), and \(CD=x\). Substitute these into the proportion: \(\frac{15}{20}=\frac{x}{15}\).

Step3: Solve for \(x\)

Cross - multiply: \(20x = 15\times15\). Then \(20x=225\). Divide both sides by 20: \(x=\frac{225}{20}=\frac{45}{4}\).

Answer:

C. \(\frac{45}{4}\)