Question

In an equilateral triangle PQR, PS is perpendicular to seg QR. Then PS²?

Answer 1

Answer:

Here,

• ∆PQR is an equilateral triangle (a triangle where all the angles and sides are same).
• PS is perpendicular to line segment QR.

Main Aim :

To find the value of PS².

Procedure:

(Look in the attachment)

As, PS is perpendicular to line segment QR, it forms two right angled triangles named ∆PSR and ∆PSQ.

According to the Pythagoras Theorem,

Hypotenuse² = Base² + Altitude²

Hence, REQUIRED ANSWER:

In triangle ∆PSR:

PS² = SR² + PR²

In triangle ∆PSQ:

PS² = SQ² + QP²

More about Pythagoras:

Pythagoras was a Greek Mathematician known for worshipping numbers. He introduced the formulae above, i.e. Hypotenuse² = Base² + Altitude². (Note: This formulae is only be applied on Right Angled Triangle)