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

Question

2882 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-27T13:03:15

See below.

enter image source here

Area of triangle is $\frac{1}{2} base \times height$ $1/2"base"xx"height"$

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

Using the sine function:

$sin (30) = \frac{opposite}{hypotenuse} = \frac{h}{x}$ $sin(30)="opposite"/"hypotenuse"=h/x$

Therefore:

$h = x sin (30)$ $h=xsin(30)$

base = 2x:

$Area = \frac{1}{2} (2 x) x sin (30) = A$ $"Area" = 1/2(2x)xsin(30)=A$

$\frac{1}{2} (2 x^{2}) sin (30) = A$ $1/2(2x^2)sin(30)=A$

$sin (30) = \frac{1}{2}$ $sin(30)=1/2$

$:.$

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

$1/2x^2=A$

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