In fig.∠ABC = 90° and BD⊥AC. If BD = 8 cm, and AD = 4 cm, find CD – InterviewSolution

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1.

In fig.∠ABC = 90° and BD⊥AC. If BD = 8 cm, and AD = 4 cm, find CD.

Answer»

Given,

∠ABC = 90° and BD⊥AC

BD = 8 cm

AD = 4 cm

Required to find: CD.

We know that,

ABC is a right angled triangle and BD⊥AC.

Then, ΔDBA∼ΔDCB [By AA similarity]

\(\frac{BD}{CD}\) = \(\frac{AD}{BD}\)

BD² = AD x DC

(8)² = 4 x DC

DC = \(\frac{64}{4}\) = 16 cm

Therefore, CD = 16 cm

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