A median of a triangle is a line segment joining any vertex to the midpoint of the opposite side.
Look at the figure given below. AD is a median of ΔABC.

Area of ΔABC = 60 cm², AD = 12 cm and AE = 10 cm. What is DC?

(A) 3 cm                (B) 5 cm                     (C) 6 cm                    (D) 10 cm

Dear Student,

Please find below the solution to the asked query:

Given : The area of triangle ABC= 60 cm² and we know area of triangle  = $\frac{1}{2}$ $\times$ Base $\times$  Height

For triangle ABC , Base = BC and Height  = AE = 10 cm ( Given ) , So


$\frac{1}{2}$$\times$ BC $\times$ AE  =  Area of the triangle ABC ,

$\frac{1}{2}$$\times$ BC $\times$ 10  = 60 ,

BC $\times$ 5 = 60 ,

BC = 12 cm

As given AD is median of triangle ABC and we know median is a line segment joining any vertex to the midpoint of the opposite side .  So  

D is mid point of BC , Then

BD  =  DC  =  $\frac{\mathrm{BC}}{2}$ ,

Thus

DC  =  $\frac{\mathrm{BC}}{2} = \frac{12}{2}$ = 6 cm 
So,

Option ( C )                                                        ( Ans )


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