area of traingle
In the following diagram AD bisects angle BAC. The area of the triangle ABD is 30 sq. cm and AC is 3 times AB. Find the area of triangle ABC.
i think the correct answer is 300 sq cm(30+30*3^2)
n/a
As it says in the question itself, AD bisects the angle BAC. Moreover, AC is 3times AB.
Area of traingle ABD = 30 = 0.5 * AD *BD
BD = 60/AD
Area of ABC = 0.5 * AD * BC
(You can prove triangle ABC is similar to ABD, Thus when AC = 3AB, then DC = 3BD. AC = BD +DC.
AC = 4BC)
Area of ABC = 0.5* AD * BC
= 0.5*AD*4BD
=0.5*AD*4*(60/AD)
=120
This is how the answer can be done
AD is the bisector. Hence it divides the opposite side in the ratio as the sides. AC is 3 times AB. Hence DC is 3 times BD. Hence the area of ADC is 3 times that of ABD. AD is the common base. Hence 120.
ans is 120(90+30) use 1/2absinC formula for triangle areas.