In each figure, there are two similar triangles. Find the unknown measurement. Give approximations to the nearest tenth.

Verified step by step guidance

1. Identify the corresponding sides of the two similar triangles. Since the triangles are similar, their corresponding sides are proportional.
2. Set up a proportion using the lengths of the known sides from both triangles. For example, if side \(a\) in the smaller triangle corresponds to side \(A\) in the larger triangle, and side \(b\) corresponds to side \(B\), then write the proportion as \(\frac{a}{A} = \frac{b}{B}\).
3. Substitute the known side lengths into the proportion, leaving the unknown measurement as a variable (e.g., \(x\)).
4. Solve the proportion equation for the unknown variable by cross-multiplying and isolating the variable on one side of the equation.
5. Calculate the value of the unknown measurement and round your answer to the nearest tenth as requested.

Key Concepts

Similarity of Triangles

Two triangles are similar if their corresponding angles are equal and their corresponding sides are proportional. This means one triangle is a scaled version of the other, which allows us to set up ratios between corresponding sides to find unknown lengths.

Proportionality of Corresponding Sides

In similar triangles, the ratios of the lengths of corresponding sides are equal. This property enables solving for unknown side lengths by setting up and solving proportion equations based on known side measurements.

Rounding and Approximation

When calculating unknown measurements, the results may be irrational or decimal numbers. Rounding to the nearest tenth means adjusting the value to one decimal place, which simplifies the answer while maintaining reasonable accuracy.