question

$abc$ is similar to $xyz$. the lengths of two sides of each triangle are given in the figure. find the length of side $x$.

* enter a fraction or a mixed number.

provide your answer below:

$x = $

Question

question

$abc$ is similar to $xyz$. the lengths of two sides of each triangle are given in the figure. find the length of side $x$.

* enter a fraction or a mixed number.

provide your answer below:

$x = $

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Proportional Reasoning" ], "new_concepts": [], "current_concepts": [ "Proportional Reasoning", "Similar Triangles" ] } ## Set up the similarity proportion $$ \frac{BC}{YZ} = \frac{AB}{XY} $$ ## Substitute the given values $$ \frac{7}{x} = \frac{8}{2\frac{2}{3}} $$ ## Solve for x $$ \begin{aligned} 2\frac{2}{3} &= \frac{8}{3} \ \frac{7}{x} &= \frac{8}{\frac{8}{3}} \ \frac{7}{x} &= 3 \ x &= \frac{7}{3} = 2\frac{1}{3} \end{aligned} $$ $ABC$ is similar to $XYZ$. The lengths of two sides of each triangle are given in the figure. Find the length of side $x$. * Enter a fraction or a mixed number. Provide your answer below: $x =$ $2\frac{1}{3}$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Similar Triangles" ] }

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QUESTION IMAGE

Question

Explanation:

Set up the similarity proportion

Substitute the given values

Solve for x

Answer: