Question

PQR is an equilateral triangle with PM perpendicular to QR.Show that Ar.(PQM)=Ar.(PRM)

Answer 1

Given : 
ΔPQR is an equilateral traingle.

To prove :
ar (PQM) = ar (PRM)

Proof :
As ΔPQR is an equilateral traingle , 
PQ = QR = PR

In Δ PQM and ΔPRM , 

PQ = PR (Given)
PM = PM (Common)
∠PMR =∠PMQ (Each 90°)

∴ Δ PQM ≅ ΔPRM [ RHS Rule ]

∴ ar (PQM) = ar (PRM

hope this is useful :)

Answer 2

PM is perpendicular to QR
angle PMQ= angle PMR=90...(1)
ln ∆ PMQ and∆PMR
angle PMQ = angle PMR.... from (1)
PQ=PR........sides of eqilateral ∆
.
. . ∆PMQ=∆PMR.......by hypotenuse side theorem
.
. . A(∆PMQ)=A(∆PMR).