Question

in a triangle ABC,AB =8cm ,BC=7cm ,AC=6cm
D,E and F are midpoints of AB,BCand CA respectively
find the lengths of the sides of triangle DEF

Answer 1

10.6 cm

Step-by-step explanation:

Midpoint Theorem:

The line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is congruent to one half of the third side.

AB = 8 cm

⇒ AD = DB = 8 ÷ 2 = 4cm

BC = 7.2 cm

⇒ BE = EC = 7.2 ÷ 2 = 3.6 cm

AC = 6 cm

⇒ AF = FC = 6 ÷ 2 = 3 cm

Apply the Midpoint Theorem:

DF = BE = 3.6 cm

DE = FC = 3 cm

EF = DB = 4 cm

Find the perimeter:

Perimeter = 3.6 + 3 + 4 = 10.6 cm

Answer: 10.6

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