Question

if these two shapes are similar, what is the measure of the missing length c? 8 m c 1 m 2 m c = \square meters submit work it out not feeling ready yet? these can help: solve proportions

Explanation:

Step1: Identify the ratio of sides

For similar shapes, the ratios of corresponding sides are equal. The green shape has sides 2 m and 1 m, and the orange shape has a side 8 m (corresponding to 2 m) and missing side \( c \) (corresponding to 1 m). The ratio of the sides of the green shape is \( \frac{2}{1} \), and for the orange shape, the ratio should be the same. So we set up the proportion \( \frac{8}{c}=\frac{2}{1} \) (or alternatively, since the other pair: \( \frac{2}{8}=\frac{1}{c} \) by matching corresponding sides).

Step2: Solve the proportion

Using cross - multiplication for \( \frac{2}{1}=\frac{8}{c} \), we get \( 2\times c = 8\times1 \), which simplifies to \( 2c = 8 \). Then divide both sides by 2: \( c=\frac{8}{2}=4 \). Or using \( \frac{2}{8}=\frac{1}{c} \), cross - multiplying gives \( 2c = 8\times1 \), same result.

Answer:

\( c = 4 \) meters