Question

If pqr is a equilateral triangle px perpendicular to qr px^2 =?

Answer 1

3a/4 is the answer is px^2

Answer 2

Answer:

$PX^2=\frac{3PR^2}{4}$

Step-by-step explanation:

Given: Δ PQR is a Equilateral triangle.

          PX is perpendicular to QR.

To find: PX²

Figure is attached.

Δ PQR is Equilateral triangle

⇒ PQ = QR = PR

Also, In Equilateral triangle Perpendicular on a  side is median of that side.i.e., PX is also median.

⇒ QX = XR = $\frac{QR}{2}$

In Δ PXR

By Pythagoras Theorem,

$PR^2=PX^2+XR^2$

$PR^2=PX^2+(\frac{QR}{2})^2$

$PR^2=PX^2+(\frac{PR}{2})^2$    ( ∵ PR = QR )

$PR^2=PX^2+\frac{PR^2}{4}$

$PX^2=PR^2-\frac{PR^2}{4}$

$PX^2=\frac{4PR^2-PR^2}{4}$

$PX^2=\frac{3PR^2}{4}$

Therefore, $PX^2=\frac{3PR^2}{4}$