Question

In APQR, if ST || QR, then RT (PQ + PS) equals
(1) PR + SQ + PT
(2) SQ (PR + PT)
(3) 2(PR + PT)
(4) PR (SQ + 2PT)​

Answer 1

Answer:

PQR is a triangle. ST is parallel to QR

By basic proportionality theorem in ΔPQR

PSPQ=PTPR

By componendo and dividendo

PSPQ=PTPR⇒PQ−PSPQ+PS=PR−PTPR+PT

SQPQ+PS=TRPR+PT

RT(PQ+PS)=SQ(PR+PT)