Question

A rectangle has length ( 4y³ + 2x² ) units and breadth ( 2y³ - 2x² ). Find its area and perimeter.​

Answer 1

Answer:

Correct option is

A

2(l+b)

Perimeter of a rectangle is the sum of all its four sides.

Since, two sides measure l and the other two sides measure b , Perimeter of a rectangle whose length(l) and breadth(b) are given, is l+b+l+b=2(l+b)

Answer 2

Answer :-

• The perimeter of the rectangle = 12y³ units.

• The area of the rectangle = 8y³ - 4x²y³ - 4x⁴ units.

To find :-

• The perimeter and area of the rectangle.

Step-by-step explanation :-

• First, let's find the perimeter of the rectangle!

We know that :-

$\underline{ \boxed{\sf Perimeter_{(rectangle)} = 2 \: (Length + Breadth)}}$

Here,

• Length = (4y³ + 2x²) units.
• Breadth = (2y³ - 2x²) units.

Therefore,

$\rm Perimeter = 2 \: ({4y}^{3} + {2x}^{2} + {2y}^{3} - {2x}^{2} )$

$\rm Perimeter = 2 \: ( {6y}^{3} + {2x}^{2} - {2x}^{2} )$

$\rm Perimeter = 2 \: ( {6y}^{3} )$

$\rm Perimeter = {12y}^{3} \: units$

Hence :-

• The perimeter of the rectangle is 12y³ units.

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• Now, let's find the area of the rectangle!

We know that :-

$\underline{ \boxed{\sf Area_{(rectangle)} = Length \times Breadth}}$

Here,

• Length = (4y³ + 2x²) units.
• Breadth = (2y³ - 2x²) units.

Therefore,

$\rm Area = ({4y}^{3} + {2x}^{2} ) \: ( {2y}^{3} - {2x}^{2} )$

$\rm Area =({4y}^{3})( {2y}^{3} ) + ( {4y}^{3}) ( { - 2x}^{2} ) + ({2x}^{2}) ( {2y}^{3} ) + ( {2x}^{2} )( { - 2x}^{2} )$

$\rm Area = {8y}^{3} - {8x}^{2} {y}^{3} + {4x}^{2} {y}^{3} - {4x}^{4}$

$\rm Area = {8y}^{3} - {4x}^{2} {y}^{3} - {4x}^{4} \: units$

Hence :-

• The area of the rectangle is 8y³ - 4x²y³ - 4x⁴ units.

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