Question

ΔPQR is an equilateral triangle.
PS⊥QR
Prove $PS^{2}=3(QS)^{2}$

Answer 1

Given:- PQR is an equilateral triangle.

in which PS perpendicular to QR.

To Proove:-PS^2=3QS^2.

Proof:-In rt. triangle.PSQ by pythagoras theorem,

PQ^2=PS^2+QS^2

QR^2=PS^2+QS^2 (PQ=QR)

PS^2=(2QS )^2-QS^2 (we can write QR as 2×QS)

PS^2=4QS^2-QS^2

PS^2=3QS^2 (hence proved)

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Answer 2

Step-by-step explanation:

️PQR IS EQUILATERAL TRIANGLE. SEG PS IS PERPENDICULAR TO SEG QR. PROVE. PS²=3QS²