1.

In a triangle ABC, AD is angle bisector of ∠A and AB : AC = 3 : 4. If the area of triangle ABC is 350 cm2, then what is the area (in cm2) of triangle ABD?1). 1502). 2003). 2104). 240

Answer»

We know that, the RATIO of the length of the line segment BD to the length of segment DC is equal to the ratio of the length of side AB to the length of side AC

⇒ AC/AB = CD/BD

⇒ CD/BD = 4/3

ALTITUDE of ?ACD = Altitude of ?ADB = Altitude of ?ABC = h

So, their areas would be in the ratio of their bases

⇒ Ar(?ACD)/ Ar(?ABD) = 4/3

Let Ar(?ACD) = 4a and Ar(?ABD) = 3A

⇒ Ar(?ACD) + Ar(?ABD) = Ar(?ABC)

⇒ 4a + 3a = 350

⇒ 7a = 350

⇒ a = 50

So, area (in cm2) of triangle ABD = 3a = 150 cm2


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