In △ABC, 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 $\frac{1}{2}$(DE + EF + DF) is:
Answer & explanation
Correct answer: option 2
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D, E and F are the midpoints of sides AB, BC and CA, respectively.
So, ( DE + EF + DF ) = \(\frac{1}{2}\) × (AB + BC + CA )
= \(\frac{1}{2}\) × (12 + 20 + 15 )
= \(\frac{1}{2}\) × (47 )
= 23.5
Now, \(\frac{1}{2}\) × ( DE + EF + DF ) = \(\frac{1}{2}\) × 23.5
= 11.75 cm