Quantitative Aptitude – Algebra – Maxima Minima – If three sides of a rectangular
Quantitative Aptitude – Algebra – Maxima Minima
Question
If three sides of a rectangular park have a total length 400 ft, then the area of the park is maximum when the length (in ft) of its longer side is
Answer
200
Solution
From CAT 2017 – Quantitative Aptitude – Algebra – Maxima Minima, we can see that,
Let a and b be the two sides of a rectangle.
a + 2b = 400
Area of rectangle = ab (We have to maximize it)
b = (400-a)/2
Put the value of b in area of rectangle.
a(400-a)/2 = (400a-a^2)/2
On differentiating the above equation, we get
400-2a = 0 => a=200
b = 100
Area will be max when length of longer side = 200.
Answer: 200
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