In given figure D, E and F are midpoint of sides BC, CA and AB respect

1.	In given figure D, E and F are midpoint of sides BC, CA and AB respectively. If AB = 4.3 cm, BC = 5.6 cm and AC = 3.9 cm then find perimeter of thefollowing:(i) ∆DEF and(ii) quadrilateral BDEF.
Answer» We know that line segment joining the mid-points of two sides is half the third side. Thus in ∆DEF, DE = 1/2AB EF = 1/2BC DF = 1/2AC ∴ Perimeter of ∆DEF = DE + EF + DF = 1/2AB + 1/2BC + 1/2AC = 1/2(AB + BC + AC) = 1/2(4.3 + 5.6 + 3.9) = 1/2(13 . 8) = 6.9 cm (ii) Perimeter of quadrilateral BDEF = BD + DE + EF + 8F = 1/2BC + 1/2AB + 1/2BC + 1/2AB = AB + BC = 4.3 + 5.6 = 9.9 cm

In given figure D, E and F are midpoint of sides BC, CA and AB respectively. If AB = 4.3 cm, BC = 5.6 cm and AC = 3.9 cm then find perimeter of thefollowing:(i) ∆DEF and(ii) quadrilateral BDEF.

Answer»

We know that line segment joining the mid-points of two sides is half the third side.

Thus in ∆DEF,

DE = 1/2AB

EF = 1/2BC

DF = 1/2AC

∴ Perimeter of ∆DEF = DE + EF + DF

= 1/2AB + 1/2BC + 1/2AC

= 1/2(AB + BC + AC)

= 1/2(4.3 + 5.6 + 3.9)

= 1/2(13 . 8)

= 6.9 cm

(ii) Perimeter of quadrilateral BDEF = BD + DE + EF + 8F

= 1/2BC + 1/2AB + 1/2BC + 1/2AB

= AB + BC

= 4.3 + 5.6

= 9.9 cm