isi-entrance 2011 Q16

isi-entrance · India · solved Vectors Introduction & 2D Area Computation Using Vectors

Suppose $ABCD$ is a parallelogram and $P, Q$ are points on the sides $BC$ and $CD$ respectively, such that $PB = \alpha BC$ and $DQ = \beta DC$. If the area of the triangles $ABP$, $ADQ$, $PCQ$ are 15, 15 and 4 respectively, then the area of $APQ$ is
(a) 14
(b) 15
(c) 16
(d) 18.

(C) From the given areas: $\beta = \alpha$, and $15\alpha^2 - 34\alpha + 15 = 0$ giving $\alpha = 3/5$. Area of parallelogram $= 50$. Area of triangle $APQ = 50 - (15+15+4) = 16$.

Suppose $ABCD$ is a parallelogram and $P, Q$ are points on the sides $BC$ and $CD$ respectively, such that $PB = \alpha BC$ and $DQ = \beta DC$. If the area of the triangles $ABP$, $ADQ$, $PCQ$ are 15, 15 and 4 respectively, then the area of $APQ$ is\\
(a) 14\\
(b) 15\\
(c) 16\\
(d) 18.

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