Question : Triangle ABC and DEF are similar. If AB = 92 cm, BC = 48 cm, AC =120 cm, and the length of the smallest side of triangle DEF is 200 cm, then find the length of the longest side of triangle DEF.
Option 1: 400 cm
Option 2: 225 cm
Option 3: 350 cm
Option 4: 500 cm
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Correct Answer: 500 cm
Solution :
Given $\triangle$ABC ~ $\triangle$DEF,
⇒ $\frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF}$
⇒ $\frac{BC}{EF} = \frac{AC}{DF}$
⇒ $\frac{48}{200} = \frac{120}{DF}$
⇒ $DF = \frac{200 \times 120}{48}$
⇒ $DF = 500$ cm
So, the length of the longest side of triangle DEF is 500 cm.
Hence, the correct answer is 500 cm.
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