Question

PQ= x cm PR= 2xcm Angle QPR= 30 degrees The area of the triangle PQR= Acm squared Show that x = square root 2A?

Answer 1

See below.

Explanation:

Area of triangle is `1/2"base"xx"height"`

From the diagram we can see we need to find h:

Using the sine function:

`sin(30)="opposite"/"hypotenuse"=h/x`

Therefore:

`h=xsin(30)`

base = 2x:

`"Area" = 1/2(2x)xsin(30)=A`

`1/2(2x^2)sin(30)=A`

`sin(30)=1/2`

`:.`

`1/2(2x^2)(1/2)=A`

`1/2x^2=A`

`x^2=2A=>x=sqrt(2A)`