Question

similarity
what is the value of x + y?
triangle with segments: x, 12, 5, y, 8, 18
a 17.5
b 18.3
c 13.6
d 22.8

Explanation:

Step1: Use the property of similar triangles (proportional sides)

Since the two triangles are similar, we have \(\frac{x}{x + 5}=\frac{12}{12 + 8}\). Cross - multiply: \(8x=5\times12\), so \(x = 7.5\).

Step2: Use the property of similar triangles for the side \(y\)

Also, \(\frac{y}{18}=\frac{12}{12 + 8}\). Cross - multiply: \(20y=18\times12\), so \(y = 10.8\).

Step3: Calculate \(x + y\)

\(x + y=7.5+10.8 = 18.3\)

Answer:

B. \(18.3\)