Question

How many rectangles with sides of measures can be drawn with 36 cm as perimeter? Also , find the dimensions of the rectangle whose area is maximum.

Answer 1

Let the other side of the rectangle be x. Then,

2(x+y) = 20

x+y = 10

y = 10 - x (we express the other side in terms of x)

A = x(10-x) = -x^2 +10x

A will be maximized when the rectangle has equal sides, hence a square. Remember that every square is also a rectangle.

maximum area is 5*5 = 25 m^2

Answer 2

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Let the other side of the rectangle be x. Then,

2(x+y) = 20

x+y = 10

y = 10 - x (we express the other side in terms of x)

A = x(10-x) = -x^2 +10x

A will be maximized when the rectangle has equal sides, hence a square. Remember that every square is also a rectangle.

maximum area is 5*5 = 25 m^2

Answer 3

$\huge\mathcal\colorbox{lime}{{\color{b}\huge\ \: {Aɴsᴡᴇʀ \: }}}$

Let the other side of the rectangle be x. Then,

2(x+y) = 20

x+y = 10

y = 10 - x (we express the other side in terms of x)

A = x(10-x) = -x^2 +10x

A will be maximized when the rectangle has equal sides, hence a square. Remember that every square is also a rectangle.

maximum area is 5*5 = 25 m^2

Answer 4

$\huge\mathcal\colorbox{lime}{{\color{b}\huge\ \: {Aɴsᴡᴇʀ \: }}}$

Let the other side of the rectangle be x. Then,

2(x+y) = 20

x+y = 10

y = 10 - x (we express the other side in terms of x)

A = x(10-x) = -x^2 +10x

A will be maximized when the rectangle has equal sides, hence a square. Remember that every square is also a rectangle.

maximum area is 5*5 = 25 m^2