Question

a segment ab is partitioned as shown. complete the statement. the ratio of $\frac{ar}{ab}$ is

Explanation:

Step1: Count segments

Count the number of equal - length sub - segments between \(A\) and \(R\) and between \(A\) and \(B\). Let's assume each sub - segment has a length of \(1\) unit. From \(A\) to \(R\), there are \(3\) sub - segments (\(AP\), \(PL\), \(LR\)). From \(A\) to \(B\), there are \(7\) sub - segments (\(AP\), \(PL\), \(LR\), \(RM\), \(MG\), \(GS\), \(SB\)).

Step2: Calculate ratio

The ratio of two lengths is the number of units of the first length divided by the number of units of the second length. So, the ratio \(\frac{AR}{AB}=\frac{3}{7}\).

Answer:

\(\frac{3}{7}\)