**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

## Download CAT 2017 Question Paper with answers and detailed solutions in PDF

## CAT 2017 Questions from Quantitative Aptitude – Algebra

Quantitative Aptitude – Algebra – Maxima Minima – Q1: If a, b, c, and d are integers such that a + b + c + d = 30, then the minimum possible value of (a – b)^2 + (a – c)^2 + (a – d)^2 is

Quantitative Aptitude – Algebra – Maxima Minima – Q2: An elevator has a weight limit of 630 kg. It is carrying a group of people of whom the heaviest weighs 57 kg and the lightest weighs 53 kg. What is the maximum possible number of people in the group?

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