In ∆ABC, AB = 5 cm, BC = 8 cm and CA = 7 cm. If D and E are respectively the mid-points of AB and BC, determine the length of DE.

Given: AB = 5 cm

BC = 8 cm

CA = 7 cm

The Midpoint Theorem states that the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side.

By the midpoint theorem,

DE = �AC

⇒ DE = � × 7 cm

⇒ DE = 3.5 cm

Hence, the length of DE = 3.5 cm