Question

D and E are the midpoints of the sides AB and AC respectively of ∆ABC if the perimeter of the ∆ABC=35cm find the perimeter of ∆ADE

Answer 1

In a triangle the line joining the mid points of the two side of this triangle is half the third side. In the given problem ∆ABC is triangle D is the midpoint of AB and E is the midpoint of AC. So the line joining D and E that is DE divide the ∆ABC into two regions, one is ∆ADE and other is quadrilateral DECB. Then DE=1/2(BC)

If perimeter of ∆BC =AB+AC+BC =35

Perimeter of ∆ADE = AD+ AE +DC=1/2 (AB) + 1/2(AC) + 1/2(BC) = 1/2(AB+AC+BC)=1/2(35)=17.5cm

Perimeter of ∆ADE is half of perimeter of∆ABC