Question

3/22 EXERCISE 9.2 Q. 1. In the Fig., ABCD is a parallelogram; AE IDC and CF1 AD. If AB = 16 cm, AE = 8 cm and CF = 10 cm, find AD. A 16 cm B 8 cm FI 10 cm DE C​

Answer 1

AD = 12.8 cm

Given:

AB = 16 cm

AE = 8 cm

CF = 10 cm

AE ⊥ CD

CF ⊥ AD

In the parallelogram ABCD, CD = AB = 16 cm [the opposite sides of the parallelogram are equal]

∵We know that area of a parallelogram = Base × Corresponding altitude

∴ Area of a parallelogram ABCD = CD × AE = AD × CF

CD and AD act as the base and AE perpendicular to CD, CF perpendicular to AD are the corresponding altitudes.

∴ AD = (CD × AE) / CF

Substituting the values for AE, CF, and CD, we get AD = (16 × 8) /10 cm = 12.8 cm

Hence, the length of AD is 12.8 cm.