Question

verify that ( \triangle pqr sim \triangle mlk ) by finding the scale factor from ( \triangle pqr ) to ( \triangle mlk ). if the triangles are not similar, enter none.
( \triangle pqr: pq = 16, qr = 24, pr = 36 )
( \triangle mlk: ml = 12, lk = 18, mk = 27 )

Explanation:

Step1: Calculate the ratio of corresponding sides

For \(PQ\) and \(ML\): \(\frac{PQ}{ML}=\frac{16}{12}=\frac{4}{3}\)
For \(QR\) and \(LK\): \(\frac{QR}{LK}=\frac{24}{18}=\frac{4}{3}\)
For \(PR\) and \(MK\): \(\frac{PR}{MK}=\frac{36}{27}=\frac{4}{3}\)

Answer:

Since the ratios of all corresponding sides are equal (\(\frac{4}{3}\)), \(\triangle PQR\sim\triangle MLK\) and the scale factor from \(\triangle PQR\) to \(\triangle MLK\) is \(\frac{3}{4}\) (because scale factor from \(\triangle PQR\) to \(\triangle MLK\) is \(\frac{ML}{PQ}=\frac{12}{16}=\frac{3}{4}\), \(\frac{LK}{QR}=\frac{18}{24}=\frac{3}{4}\), \(\frac{MK}{PR}=\frac{27}{36}=\frac{3}{4}\))