How to find if two acute / obtuse triangles are similar

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PSAT Math › How to find if two acute / obtuse triangles are similar

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$\text{Triangle A}$ and $\text{Triangle B}$ are similar triangles. The perimeter of Triangle A is 45” and the length of two of its sides are 15” and 10”. If the perimeter of Triangle B is 135” and what are lengths of two of its sides?

${30}''\textup{ and }{45}''$

${13}''\textup{ and }{19}''$

${20}''\textup{ and }{30}''$

${4}''\textup{ and }{6}''$

Explanation

The perimeter is equal to the sum of the three sides. In similar triangles, each side is in proportion to its correlating side. The perimeters are also in equal proportion.

Perimeter A = 45” and perimeter B = 135”

The proportion of Perimeter A to Perimeter B is $\frac{45}{135}=\frac{1}{3}$ .