The perimeter of two similar triangles RST and IJK (in correspondence) are 64 cm and 56 cm respectively. If IJ = 16 cm, then what is the length of RS?

14 cm

Concept Used

The ratio of the perimeter of 2 similar triangles is equal to the ratio of the corresponding sides.

\(\frac{Perimeter\; of\; ABC}{Perimeter\;of\;PQR}\) = \(\frac{AB}{PQ}\) = \(\frac{BC}{QR}\) = \(\frac{AC}{PR}\)

Calculation

\(\Delta \)ABC and \(\Delta \)PQR are similar so

\(\frac{AB}{PQ}\) = \(\frac{Perimeter\; of\; ABC}{Perimeter\;of\;PQR}\)

\(\frac{16}{PQ}\) = \(\frac{64}{56}\)

PQ = 14 cm

Therefore, PQ is 14 cm.