In Fig. 12.5, ΔABC has sides AB = 7.5 cm, AC = 6.5 cm and BC = 7 cm. On base BC a parallelogram DBCE of same area as that of ΔABC is constructed. Find the height DF of the parallelogram.

a = 6.5, b = 7, c = 7.5

s = (a + b + c)/2

⇒ s = (6.5 + 7 + 7.5)/2 = 21/2 = 10.5

Area(Δ) = √s(s-a)(s-b)(s-c)

⇒ Area(Δ) = √10.5(10.5-6.5)(10.5-7)(10.5-7.5)

⇒ Area(Δ) = √10.5×4×3.5×3

⇒ Area(Δ) = 21 cm²

Area of parallelogram (BCED) = Area (Δ)

⇒ BC × DF = 21

⇒ 7 × DF = 21

⇒ DF = 3 cm