Question

part: a
consider the similar triangles below:
(there are two triangles drawn, the first with vertices a, b, c: ab=4, bc=6, ac=7; the second with vertices p, q, r: qr=12, angles at b and q are marked equal, angles at a and p are marked equal)
part: b
find the length of side pr?

Explanation:

Step1: Identify corresponding sides

Since triangles \(ABC\) and \(PQR\) are similar, the ratios of corresponding sides are equal. Side \(BC = 6\) corresponds to side \(QR = 12\), and side \(AC = 7\) corresponds to side \(PR\), side \(AB = 4\) corresponds to side \(QP\) (though we use \(BC\) and \(QR\) for the ratio).

Step2: Calculate the scale factor

The scale factor from \(\triangle ABC\) to \(\triangle PQR\) is \(\frac{QR}{BC}=\frac{12}{6} = 2\).

Step3: Find length of \(PR\)

Since \(AC\) corresponds to \(PR\), we multiply \(AC\) by the scale factor. So \(PR=AC\times2 = 7\times2=14\).

Answer:

14