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.

he area of ΔABC is, 1787.06 inches2

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,