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Question

The adjacent sides of a rectangle with a given perimeter is 100cm and enclosing maximum area are.


A

10cmand40cm

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B

20cmand30cm

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C

25cmand25cm

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D

15cmand35cm

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Solution

The correct option is C

25cmand25cm


Explanation for the correct option:

Find the adjacent sides of the rectangle.

Step 1: Given information

Let us assume that,

The adjacent side of rectangle is xandy.

The perimeter of rectangle is 2(sumoftwoadjacentsideslength)

Then the parameter can be expressed as,

2x+y=100cmx+y=50cmy=50-x

Step 2: Finding dAdx

Since, the area of rectangle is product of two adjacent sides.

The area of the rectangle can be expressed as,

A=xyA=x50-xA=50x-x2

Differentiate the above Equation

dAdx=50-2x

Step 3: Finding the maximum area

For the maximum area can be expressed as,

dAdx=0

Then,

50-2x=0-2x=-50x=502x=25

Therefore, getting the value of y

y=50-xy=50-25y=25

Hence, option (C) is the correct answer.


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