In ΔABC, D, E, and F are the midpoints of sides AB, BC, and CA, respectively. If AB = 12 cm, BC = 20 cm and CA = 15 cm, then the value of (1/2)(DE + EF + DF) is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 11.75 cm
By the midpoint theorem,
⇒ DF = (1/2)BC
Similarly,
⇒ EF = (1/2)AB
⇒ DE = (1/2)AC
⇒ (1/2)(DE + EF + DF)
⇒ (1/2)(6 + 10 + 7.5)
⇒ 23.5/2
⇒ 11.75 cm