What will be the max area of a rectangle if its parameter is 36 cm?

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07 May 2010 max area of rectangle?

What will be the max area of a rectangle if its parameter is 36 cm?

OPtion

1) 64
2) 72
3) 81
4) 100
5) 110
6) 80
7) 77
8) 72
9) 24
10) 65

Solution

All square are rectangle. so for the max area all side will be 9 cm
and area will become 9*9 = 81 cm^2

Correct Option: 3 Best Solution (7)

Saswata Chakraborty   14 years AGO

2(a+b)=36
a+b=18....only possibility a=b=9..area=81

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Sanoj   14 years AGO

its and square of 9X9
area will be 81

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Dr.Dipin Singh   14 years AGO

sum of two sides = 36/2=18 cms.

Area of rectangle is max when sides are equal .

Means each side = 18/2= 9 cm

Area = 9*9=81 sq cms

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Karan   14 years AGO

each side = 36/4=9 cms

Area=9*9=81 sq cms

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SUDESHNA SEN   14 years AGO

Let the height and width of the rectangle be a and b, respectively.
Therefore, 2(a+b)= 36, or, (a+b)=18, or b=(18-a)
so, we have to maximize ab, given that b=(18-a).
Max. ab= a(18-b)= 18a-b^2
By first order condition, we have da/d[a(18-a)]=0
or, 18-2a=0
or, 2a=18,
or, a=9. and b= 18-9=9
Therefore, the max area of the rectangle= ab= 9*9=81 sq c.m...... Option 3)

Like? Yes (1) | No   

ASHOK ROY   14 years AGO

Let the height and width of the rectangle be a and b, respectively.
Therefore, 2(a+b)= 36, or, (a+b)=18, or b=(18-a)
so, we have to maximize ab, given that b=(18-a).
Max. ab= a(18-b)= 18a-b^2
By first order condition, we have da/d[a(18-a)]=0
or, 18-2a=0
or, 2a=18,
or, a=9. and b= 18-9=9
Therefore, the max area of the rectangle= ab= 9*9=81 sq c.m...... Option 3)

Like? Yes (1) | No   

Prashant Khare   14 years AGO

Its a square of side 9.

Like? Yes (1) | No