PB = AQ/QC = AH = AB adding 1 on SIDES we get(AP/PB) + 1 = (AQ/QC) + 1(AP + PB)/PB = (AQ + QC)/QC.AB/PB = AC/QC = AH/AOPB/AB = QC/ACBP : AB = QC : AC = AO/AHGiven, ratio of areas of triangle APQ : triangle ABC is 25 : 36\(\begin{array}{L}\Rightarrow \frac{{\frac{1}{2} \times \;AH \times BC}}{{\frac{1}{2}\; \times AO\; \times PQ}} = \frac{{25}}{{36}}\\\Rightarrow \frac{{\;AH \times BC}}{{AO\; \times PQ}} = \frac{{25}}{{36}}\end{array}\)

"> PB = AQ/QC = AH = AB adding 1 on SIDES we get(AP/PB) + 1 = (AQ/QC) + 1(AP + PB)/PB = (AQ + QC)/QC.AB/PB = AC/QC = AH/AOPB/AB = QC/ACBP : AB = QC : AC = AO/AHGiven, ratio of areas of triangle APQ : triangle ABC is 25 : 36\(\begin{array}{L}\Rightarrow \frac{{\frac{1}{2} \times \;AH \times BC}}{{\frac{1}{2}\; \times AO\; \times PQ}} = \frac{{25}}{{36}}\\\Rightarrow \frac{{\;AH \times BC}}{{AO\; \times PQ}} = \frac{{25}}{{36}}\end{array}\)

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Points P and Q lie on side AB and AC of triangle ABC respectively such that segment PQ is parallel to side BC, If the ratio of areas of triangle APQ : triangle ABC is 25 : 36. Then the ratio of AP : PB is ___.

SRMJEEE Analytical Geometry in SRMJEEE 11 months ago

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Given that PQ || BC .we know that AP/PB = AQ/QC = AH = AB adding 1 on SIDES we get(AP/PB) + 1 = (AQ/QC) + 1(AP + PB)/PB = (AQ + QC)/QC.AB/PB = AC/QC = AH/AOPB/AB = QC/ACBP : AB = QC : AC = AO/AHGiven, ratio of areas of triangle APQ : triangle ABC is 25 : 36\(\begin{array}{L}\Rightarrow \frac{{\frac{1}{2} \times \;AH \times BC}}{{\frac{1}{2}\; \times AO\; \times PQ}} = \frac{{25}}{{36}}\\\Rightarrow \frac{{\;AH \times BC}}{{AO\; \times PQ}} = \frac{{25}}{{36}}\end{array}\)

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Posted on 08 Nov 2024, this text provides information on SRMJEEE related to Analytical Geometry in SRMJEEE. Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.

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