Suppose PQ=a; QR=b; AB=l
Probability = Area of rectangle/ Area of square \(= \frac{a*b}{l^2} = \frac{a}{l}*\frac{b}{l}\)
Statement 1 Length of diagonal of rectangle \(= \sqrt{a^2+b^2}\)
Length of the diagonal of square = \(\sqrt{2}l\)
\( \frac{\sqrt{a^2+b^2}}{\sqrt{2}l}\) = \(\frac{11}{20}\)
\(\frac{a^2}{l^2} +\frac{b^2}{l^2} = \frac{121}{200}\)
.....(1)We can't find \(\frac{a}{l}\) and \(\frac{b}{l}\), using above equation
InsufficientStatement 2- We know a/b. But there is no way to find the ratios of the area of rectangle and square.
InsufficientCombining both statements\(\frac{b}{l} = \frac{5}{6}(\frac{a}{l})\) (From statement 2). Also \(\frac{a}{l}, \frac{b}{l} >0\)
Hence, we can find the unique value of \(\frac{a}{l}\) and \(\frac{b}{l}\), using equation (1) (From statement 1)
SufficientBunuel wrote:
In the figure above, rectangle PQRS is a shaded region inside the square ABCD. What is the probability that a point chosen at random from the square ABCD will lie inside the shaded rectangle PQRS?
(1) The length of a diagonal of rectangle PQRS is 55% the length of a diagonal of square ABCD
(2) The length of side PQ is 20% greater than the length of side QR
Project PS Butler
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