Question

find the unknown lengths in the pair of similar triangles. the length of a is 21 in. the length of b is in.

Explanation:

Step1: Set up proportion

Since the triangles are similar, the ratios of corresponding sides are equal. Let's assume $\triangle ABC\sim\triangle QRP$. Then $\frac{AB}{QR}=\frac{AC}{QP}=\frac{BC}{RP}$. We know $AB = 12$ in, $AC=a = 21$ in, $BC = 27$ in, $QP = 8$ in, $RP=14$ in. We use the proportion $\frac{AB}{QR}=\frac{AC}{QP}$.

Step2: Substitute values and solve for $b$

Substituting the known values into $\frac{AB}{QR}=\frac{AC}{QP}$, we have $\frac{12}{b}=\frac{21}{8}$. Cross - multiply gives $21b=12\times8$. So $21b = 96$. Then $b=\frac{96}{21}=\frac{32}{7}\approx4.57$ in.

Answer:

$\frac{32}{7}$ in