Q. 1

B is a right angle in ΔABC and is an altitude to hypotenuse. AB = 8, BC = 6. Find the area of ΔBDC.

Answer :


In ∆ABC, B is a right angle, AB = 8 and BC = 6




= 24 …(1)


In ∆ABC, B is a right angle and BD is an altitude,


In ∆ABC,


A + C = 90⁰ and,


In ∆BDC,


DBC + C = 90⁰


So, A = DBC …(2)


In ∆ABC and ∆BDC,


DAB DBC [from (2)]


ADB BDC [by right angles]


The correspondence ADB BDC is a similarity by AA corollary.


Areas of similar triangles are proportional to the squares of their corresponding sides.




…(3)


Now, ADB + BDC = ABC





BDC = 8.64


The area of ∆BDC is 8.64.


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