Maths-
General
Easy
Question
ABC is an isosceles right angled triangle with AB = BC = 1. If P is any point on BC, then min {max{(area APQ), (area PQBR), area PRC)}} is
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-
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- none of these
Hint:
find the areas of the polygons in terms of a variable and then find the minimum and maximum areas.
The correct answer is:
2/9
Length of AC = √2
Let the length of AP be x
Length of PC= √2-x
Let angle QAP=angle BCP = z
Length of AQ = APcos 45 = AP/√2
Length of PQ= AP/ √2
Area of APQ = x2/4
Area of PQBR = PQ x PR = (x/√2 )(1-x/√2)
=x/√2-x2/2
Area of PRC = ½(PR)(RC)=1/2(1-x/√2)(1-x/√2)
= x2/4 -x/√2+1/2
From the area functions, we can see that max(Area APQ, area PQBR, area PRC)= area of APQ = x2/4 when x>=2√2/3
Minimum of the areas = area of PQBR = x/√2- x2/2= 2/9
the minimum function gives us the minimum of the values passed to it . similarly, the max or maximum function returns the maximum of the values passed to it.
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