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?
Answer & explanation
Correct answer: option 4
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.