Question

In triangle xyz P is the midpoint of side y z find the ratio of their area of xyz:area of triangle xyz

Answer 1

we have a triangle XYZ , where P is the mid point of side YZ As:

Let height of triangle XYZ = h  
Here we know YP  =  PZ  =  12 YZ                     (As P is mid point of YZ)
And 
Area of triangle = 12 base * height
Area of ∆XYZ = 12 (YZ) (h)               -----------------------( 1 )
And
Area of ​ ∆XYP = 12 ( YP ) ( h)                          (Height is same as both triangle share same height vertices X)
SO,
Area of ∆XYP = ​​ 12  (​ 12 YZ) (h)

From equation 1 we get

Area of ∆XYP = ​12Area of ∆XYZ

⇒ Area of ∆ XYZArea of ∆ XYP = 21 
SO,
​Area of ∆XYZ  : ​Area of ∆XYP  = 2 : 1                  

Answer 2

The correct question is find the ratio ar (triangle xyz) :ar (triangle xyp)

we have a triangle XYZ, where P is the midpoint of side YZ as:

Let the height of triangle XYZ = h
Here we know YP = PZ = 1/2 yz (as P is midpoint of YZ)
and 
Area of triangle = 1/2 base x height
Area of triangle XYZ = 1/2 (YZ) (h) -- (1)
and Area of triangle XYP = 1/2 (YP) (h) (height is same as both triangle share same height vertices X)
So,
Area of triangle XYP = 1/2(1/2 YZ) (h)
from equation 1 we get
Area of triangle XYP = 1/2 Area of triangle XYZ

=> area of triangle XYZ/ Area of triangle XYP = 2/1

So area of triangle XYZ : Area of triangle XYP = 2:1