Question

In the figure given, \(\Delta ABC \sim \Delta XYZ\), then find the values of \(x\) and \(y\). (Given: \(AB=4, BC=6, AC=y, XY=x, YZ=7.2, XZ=6\))

Hint:

Always ensure you are pairing corresponding sides correctly. Look at the order of vertices in the similarity statement (\(ABC \sim XYZ\)) to match sides.

Answer 1

Step 1: Understanding the Concept:
When two triangles are similar, the ratios of their corresponding sides are equal.
Step 2: Key Formula or Approach:
\[ \frac{AB}{XY} = \frac{BC}{YZ} = \frac{AC}{XZ} \]
Step 3: Detailed Explanation:
Substituting the given side lengths into the ratio:
\[ \frac{4}{x} = \frac{6}{7.2} = \frac{y}{6} \]
First, simplify the known ratio:
\[ \frac{6}{7.2} = \frac{60}{72} = \frac{5}{6} \]
To find \(x\):
\[ \frac{4}{x} = \frac{5}{6} \implies 5x = 24 \implies x = \frac{24}{5} = 4.8 \]
To find \(y\):
\[ \frac{y}{6} = \frac{5}{6} \implies y = 5 \]
Step 4: Final Answer:
The values are \(x = 4.8\) and \(y = 5\).