Question

in a triangle ABC.a median AD is drawn.P is point on AD such that AP:PD=3:4.what is the ratio of area of triangle APB and triangle ABC respectively?​

Answer 1

Answer:

we know if the two triangle have same height and different base ,

then ratio of their area is equal to the ratio of their respective base .

since AD is a median

hence BD=CD

THEREFORE , area of triangle ABD= ACD ( both the triangle have same height and same base )

hence, area of ABD =1/2( AREA of ABC)———(1)

Also, area of ABP=1/3(Area of ABD)=1/3* 1/2(ABC)

HENCE Area of ABP=1/6( Area of ABC)

Answer 2

We can't divide a triangle into three parts using the points on the sides of a triangle.

So, we need to take a point inside the triangle to make three triangles from one triangles.

(A centroid of a triangle is the point where the three medians of the triangle meet. A median of a triangle is a line segment from one vertex to the mid point on the opposite side of the triangle.)

Now, to divide an scalene triangle ABC into three triangles APB,BPC,CPA of same area we need to take a point in the centre and that point is called centroid.

Centoid of △ABC is point P.

Thus, P must be in centre of △ABC.