In fig. the point s divides the side QR of triangle PQR in tye ratio l:m . Prove that ar (triangle PQS) :ar( triangle PRS=l:m
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Proved that ar (triangle PQS) :ar( triangle PRS=l:m
Step-by-step explanation:
QS = (L/(L + M) ) * QR
RS = (M/(L + M) ) * QR
Let say PA is altitude at QR
Area of Δ PQR = (1/2) QR * PA
Area of Δ PQS = (1/2) QS * PA = (1/2) (L/(L + M) ) * QR * PA
Area of Δ PRS = (1/2) RS * PA = (1/2) (M/(L + M) ) * QR * PA
Area of Δ PQS : Area of Δ PRS = (1/2) (L/(L + M) ) * QR * PA : (1/2) (M/(L + M) ) * QR * PA
= L : M
Hence proved that
ar (triangle PQS) :ar( triangle PRS=l:m
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