Question : DEF is an isosceles triangle such that DE = DF = 60 cm and EF = 96 cm. DG is a median to base EF. What is the length of DG?
Option 1: 22 cm
Option 2: 36 cm
Option 3: 24 cm
Option 4: 32 cm
Correct Answer: 36 cm
Solution : Given: DE = DF = 60 cm, EF = 96 DG median cuts EF into two halves. So, EG = $\frac{96}{2}=48$ cm In $\triangle$DEG, DE 2 = DG 2 + EG 2 ⇒ DG = $\sqrt{60^2-48^2}=\sqrt{1296}=36$ cm Hence, the correct answer is 36 cm.
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