Question

Please answer me the A3 question

Answer 1

Here is your answer :

Q. What is a rectangle ?

= A rectangle is a parallelogram whose each angle is a right angle ( 90° ).

Q. What is perimeter ?

= The continuous lines that form the boundary of a closed figure.

Properties of a rectangle :

1. Each angle is a right angle.

2. Opposite sides are equal and parralel.

3. Its diagonals are of equal length.

4. Its diagonals bisects each other.

Some useful formulas related to rectangle.

Area of rectangle = length × Breadth

Perimeter of rectangle = 2( Length + Breadth )

Diagonal of rectangle = √( length² + Breadth² )

Given,

Length of rectangle = ( 4x² + 3x - 5 )

Perimeter of rectangle = ( 2x³ + x - 3 )

Let the breadth of rectangle is y.

Using Formula,

=> Perimeter of rectangle = 2( Length + Breadth )

=> 2x³ + x - 3 = 2 ( 4x² + 3x - 5 + y )

=> ( 2x³ + x - 3 ) / 2 = ( 4x² + 3x - 5 + y )

=> [ ( 2x³ + x - 3 ) / 2 ] - ( 4x² + 3x - 5 ) = y

=> [ ( 2x³ + x - 3 ) - 2( 4x² + 3x - 5 ) ] / 2 = y

=> [ 2x³ + x - 3 - 8x² - 6x + 10 ] / 2 = y

=> [ 2x³ - 8x² - 5x + 7 ] / 2 = y

Hence , the breadth of rectangle is [ 2x³ - 8x² - 5x + 7 ] / 2.

Verification :

=> Perimeter of rectangle = 2 [ length + Breadth ]

=> 2x³ + x - 3 = L.H.S

= 2[ ( 4x² + 3x - 5 ) + ( 2x³ - 8x² - 5x + 7 )/2 ]

= 2[ 2( 4x² + 3x - 5 ) + ( 2x³ - 8x² - 5x + 7 ] / 2

= [ 8x² + 6x - 10 + 2x³ - 8x² - 5x + 7 ]

= [ 8x² - 8x² - 10 + 7 + 6x - 5x + 2x³ ]

= -3 + x + 2x³

=> 2x³ + x - 3 = L.H.S

Verified !

Hope it helps !!