Question

From the given information in the figure, prove that PM =PN=√3a

Answer 1

Hey There,


The answer is in the image.


Hope it helps
Purva
Brainly Community

Answer 2

Answer:

Step-by-step explanation:

Let PQ=QR=PR=a, thus ΔPQR is an  equilateral triangle.

Therefore, $QS=SR=\frac{1}{2}QR$

⇒$QS=\frac{a}{2}$

Also, PS is an altitude of ΔPQR, therefore $PS=\frac{\sqrt{3}}{2}a$

Now, $MS=MQ+QS$

=$a+\frac{a}{2}$

=$\frac{3a}{2}$

Thus, $MS=\frac{3a}{2}$

Now, ΔPMS is a right angled triangle, using the pythagoras theorem, we have

$PM^{2}=MS^{2}+PS^{2}$

$PM^2=(\frac{3a}{2})^2+(\frac{\sqrt{3}a}{2})^2$

$PM^2=3a^2$

$PM=\sqrt{3}a$

Since, the given figure is symmetrical, we can prove in the same way for PN.

Therefore, $PM=PN=\sqrt{3}a$

Hence proved.