in the given figure triangle ABC is equal to 90 degree and BD perpendicular to AC if BD is equal to 8 cm is equal to 4 cm find CD
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SOLUTION :
Given, BD = 8 cm, AD = 4 cm, ∠ABC = 90° and BD⊥AC.
we know that ,If a perpendicular is drawn from the vertex containing a right angle of a right triangle to the hypotenuse then the triangle on each side of the perpendicular are similar to each other and to the whole triangle.
So, ΔDBA∼ΔDCB (A-A similarity)
BD/CD = AD/BD
[Since, triangles are similar, hence corresponding sides will be proportional]
BD² = AD x DC
(8)² = 4 x DC
64 = 4DC
DC = 64/4
DC = 16
Hence, the length of CD is 16 cm..
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Answer:
16is the required answer
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