Question

In △ABC ∠ABC=90° , BD is perpendicular to AC If BD=12, AD=8 then find the length of DC *​

Answer 1

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..