Am is a median of an acute triangle abc. the distance of the point m from the side ab is 48 inches, and from ac is 40 inches, bc = 100in. find the area of abc.

Answer : The area of ΔABC is,

Step-by-step explanation :

Given:

Side AM = 48 inches

Side AC = 40 inches

Side BC = 100 inches

First we have to determine the side CM and side BM.

As, AM is a median of an acute triangle ABC. So, median divides the side BC into two equal side.

That means,

Side CM = Side BM = = 50 inches

Now we have to determine the semi-perimeter of ΔAMC.

Formula used :

Now we have to determine the area of ΔAMC.

Using Heron's formula:

where,

A is a area, s is a semi-perimeter and a, b, c are the sides of triangle.

Thus, the area of ΔAMC =

Now we have to determine the area of ΔABC.

As we know that, each median of a triangle divides the triangle into two smaller triangles which have equal area.

So,

ΔABC = 2 × ΔAMC

ΔABC =

ΔABC =

Thus, the area of ΔABC is,