Question

In ΔABC, altitudes AD and BE are drawn. If AD = 7 cm, BE = 9 cm and EC = 12 cm then, find the length of CD.

Answer 1

Given: AD = 7 cm, BE = 9 cm and EC = 12 cm

∠E = ∠D = 90°

In ΔADC and ΔBEC

∠ADC = ∠BEC     ...[90° (Given)]

∠ACD = ∠BCE     ...[Common]

By AA similarity criteria ΔADC ∼ ΔBEC

`"AD"/"BE"="CD"/"CE"`

`7/9="CD"/12`

CD = `7/9xx12`

CD = `28/3` cm