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A line cuts two sides AB and AC of triangleABC at point P and Q respectively. Prove Area of triangleAPQ/area of triangleABC =APmultiplyAQ/AB multiply AC

Answer»

LET ∠A = θ.

By the FORMULA of the AREA of TRIANGLE,

\triangle ABC=\frac{1}{2} \times AB \times AC \times sin \theta,

\triangle APQ=\frac{1}{2} \times AP \times AQ \times sin\theta.

∴ \frac{\triangle APQ}{\triangle ABC} =\frac{\frac{1}{2} \times AP \times AQ \times sin\theta}{\frac{1}{2} \times AB \times AC \times sin \theta} =\frac{AP \times AQ}{AB \times AC}


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