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Problem 269

The sides of triangle \(\mathrm{ABC}\) measure 5,7, and 9 . The shortest side of a similar triangle, $\mathrm{A}^{\prime} \mathrm{B}^{\prime} \mathrm{C}^{\prime}$, measures 10 . (a) Find the measure of the longest side of triangle $\mathrm{A}^{\prime} \mathrm{B}^{\prime} \mathrm{C}^{\prime}$. (b) Find the ratio of the measures of a pair of corresponding altitudes in triangles \(\mathrm{ABC}\) and $\mathrm{A}^{\prime} \mathrm{B}^{\prime} \mathrm{C}^{\prime}$. (c) Find the perimeter of triangle $\mathrm{A}^{\prime} \mathrm{B}^{\prime} \mathrm{C}^{\prime}$.

Expert verified

The longest side of triangle A'B'C' measures 18 units, the ratio of the measures of a pair of corresponding altitudes in triangles ABC and A'B'C' is 2, and the perimeter of triangle A'B'C' is 42 units.

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