Triangle ABC and DEF are similar. If AB = 92 cm, BC = 48 cm, AC =120 cm, and the length of the smallest side of DEF is 200 cm, then find the length of the longest side of triangle DEF?

500 cm

Concept Used

Given, \(\Delta \)ABC is similar to \(\Delta \)DEF,

Therefore,

\(\frac{AB}{DE}\) = \(\frac{BC}{EF}\) = \(\frac{AC}{DF}\)

Calculation

= \(\frac{BC}{EF}\) = \(\frac{AC}{DF}\)

= \(\frac{48}{200}\) = \(\frac{120}{DF}\)

= DF = \(\frac{200}{48}\) x 120

= DF = 500 cm

Therefore, length of DEF is 500 cm.