Question

marie and jake both set up a proportion to find the missing width, w, of the smaller of two similar rectangles. their work is shown below. maries work: \\(\frac{2}{7}=\frac{w}{6}\\) \\(7w = 8\\) \\(w \approx 1.14\\) jakes work: \\(\frac{2}{w}=\frac{7}{6}\\) \\(7w = 12\\) \\(w \approx 1.71\\) two rectangles: first has height 2, length 7; second has height 6, width w which student made an error in their work and what error did they make? \\(\bigcirc\\) marie did not set up the proportion correctly. \\(\bigcirc\\) jake did not set up the proportion correctly. \\(\bigcirc\\) marie did not multiply 2×6 correctly. \\(\bigcirc\\) jake did divide 12 by 7 correctly.

Explanation:

Step1: Identify corresponding sides

The first rectangle has height 2, width 7. The second (smaller) has height 6, width w. For similarity, ratio of heights = ratio of widths. So $\frac{2}{6} = \frac{7}{w}$ (or $\frac{2}{7} = \frac{6}{w}$).

Step2: Check Marie's proportion

Marie wrote $\frac{2}{7} = \frac{w}{6}$. This mismatches correct correspondence (height ratio ≠ width/small height).

Step3: Check Jake's proportion

Jake wrote $\frac{2}{w} = \frac{7}{6}$. Cross-multiplying gives $7w=12$, $w≈1.71$. His proportion aligns with height/width = height/width for similarity.

Step4: Evaluate options

Marie’s error is incorrect proportion setup.

Answer:

Marie did not set up the proportion correctly.