The sides of \(\triangle ABC\) are 11 cm, 15 cm and 18 cm. D, E and F are the mid-points of the sides BC, CA and AB respectively. What is the perimeter of \(\triangle DEF\)?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 22 cm
By the mid-point theorem, the segment joining the mid-points of two sides of a triangle is parallel to the third side and half of it. Each side of \(\triangle DEF\) is therefore half of one side of \(\triangle ABC\).
Perimeter of \(\triangle ABC=11+15+18=44\) cm
EF \(=\frac{1}{2}\)BC, FD \(=\frac{1}{2}\)CA, DE \(=\frac{1}{2}\)AB
Perimeter of \(\triangle DEF\displaystyle=\frac{1}{2}\times44=22\) cm
