Discussion
PQRS is a parallelogram whose diagonals PR and QS intersect at a point O such that OP = \((x + 7)\) cm, OQ = \((x + y)\) cm, OR = 20 cm and OS = 16 cm. Then, value of \((7y + 5)\) (in cm) is :
Answer: C
The value of \(7y + 5\) is 26.
The diagonals of a parallelogram bisect each other, so OP = OR and OQ = OS:
\[ \begin{aligned} x + 7 &= 20 \Rightarrow x = 13 \\ x + y &= 16 \Rightarrow y = 3 \\ 7y + 5 &= 21 + 5 = 26 \end{aligned} \]
21 is 7y without the 5. Equating OP with OQ instead of with OR, as if all half-diagonals were equal, is the usual slip behind the other values.
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