Question

i \can\ similarity
△abc ~ △xyz. find the value of x.
a 8.5
c 16
b 22.5
d 12.5

Explanation:

Step1: Find the scale factor

Since \(\triangle ABC\sim\triangle XYZ\), the ratio of corresponding sides is equal. The ratio of \(AB = 10\) to \(XY=17.5\) is the scale factor.
\(\text{Scale factor}=\frac{AB}{XY}=\frac{10}{17.5}=\frac{10\times2}{17.5\times2}=\frac{20}{35}=\frac{4}{7}\)

Step2: Set up the proportion for \(AC\) and \(XZ\)

We know \(AC = 14\) and \(XZ=x + 2\). Using the property of similar triangles \(\frac{AC}{XZ}=\frac{AB}{XY}\)
\(\frac{14}{x + 2}=\frac{10}{17.5}\)
Cross - multiply: \(10(x + 2)=14\times17.5\)
\(10x+20 = 245\)
Subtract 20 from both sides: \(10x=245 - 20=225\)
Divide both sides by 10: \(x=\frac{225}{10}=22.5\)

Answer:

B. 22.5