Questions: Triangle ABC and triangle XYZ are similar triangles. The lengths of two sides of each triangle are shown. Find the lengths of the third side of each triangle. a=□ y=□

Solution Steps

Since \(\triangle ABC\) and \(\triangle XYZ\) are similar, the corresponding sides are proportional. The sides \(AB\) and \(XY\), \(AC\) and \(XZ\), and \(BC\) and \(YZ\) correspond to each other.

Given:

• \(AB = 5\)
• \(XY = 2.5\)
• \(AC = 4.6\)
• \(XZ = 3.8\)

We need to find the lengths of \(a\) (side \(BC\)) and \(y\) (side \(YZ\)).

The scale factor \(k\) can be found using the ratio of the corresponding sides: \[ k = \frac{XY}{AB} = \frac{2.5}{5} = 0.5 \]

Since the triangles are similar, the ratio of the sides is constant: \[ \frac{BC}{YZ} = k \]

For \(\triangle ABC\): \[ a = BC = \frac{4.6}{3.8} \times 3.8 = 4.6 \times 0.5 = 2.3 \]

For \(\triangle XYZ\): \[ y = YZ = 3.8 \times 0.5 = 1.9 \]

Final Answer