Question

Draw straight line in this rectangle to divide it into 2 equal triangles. What area of each of the Triangles? is the area​

Answer 1

Answer:

Let ABC be a triangle and Let AD be one of its medians.

In △ABD and △ADC the vertex is common and these bases BD and DC are equal.

Draw AE⊥BC.

Now area(△ABD)=21×base×altitude of△ADB

=21×BD×AE

=21×DC×AE(∵BD=DC)

but DC and AE is the base and altitude of △ACD

=21× base DC × altitude of △ACD

=area△ACD

⇒area(△ABD)=area(△ACD)

Hence the median of a triangle divides it into two triangles of equal areas.  

Answer 2

Step-by-step explanation:

Let ABC be a triangle and Let AD be one of its medians.

In △ABD and △ADC the vertex is common and these bases BD and DC are equal.

Draw AE⊥BC.

Now area(△ABD)=

2

1

×base×altitude of△ADB

=

2

1

×BD×AE

=

2

1

×DC×AE(∵BD=DC)

but DC and AE is the base and altitude of △ACD

=

2

1

× base DC × altitude of △ACD

=area△ACD

⇒area(△ABD)=area(△ACD)

Hence the median of a triangle divides it into two triangles of equal areas.