Question

in triangle xyz ,xa is a median on side yz . find ratio of ar[xya]:ar[xza

Answer 1

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Answer 2

Hence ratio of ar[xya]:ar[xza] is 1:1.

Step-by-step explanation:

Given:

In triangle xyz, xa is a median on side yz.

So,

$YA=AZ=\frac{1}{2}YZ$

Let height of triangle=h cm.

Area of triangle = $\frac{1}{2}\times base\times height$

So, Area of triangle XYA= $\frac{1}{2} \times ya \times h$

And,  Area of triangle xza =$\frac{1}{2} \times za \times h$

$\frac{Area of triangle xya}{Area of triangle xza} =\frac{\frac{1}{2}\times ya\times h }{\frac{1}{2}\times za\times h}$

$\frac{Area of triangle xya}{Area of triangle xza} =\frac{ya}{za}$

                            =$\frac{ya}{ya}$  [ya=za]

                            = 1

Hence ratio of ar[xya]:ar[xza] is 1:1.