The legth of a rectangle is the same as the legth of each side of a square. The legth rectangle is 4 cm more than 3 times the width of the rectangle The area of the square is 66cm^2 more than the area of the rectangle. Find the length and the width of the rectangle

Let, length and breadth of rectangle is L and B respectively.

It is given that :

The length rectangle is 4 cm more than 3 times the width of the rectangle.

L = 3B + 4  1 )

Also, area of square = area of the rectangle + 66

L² = LB + 66

Putting value of L from

L² = ( 3B + 4 )( B ) + 66

L² = 3B²  + 4B + 66

( 3B + 4 )² = 3B²  + 4B + 66

9B² + 16 + 24B = 3B²  + 4B + 66

6B² + 20B - 50 = 0

3B² + 10B - 25 = 0

3B² + 15B - 5B -25 = 0

3B( B + 5 ) -5( B + 5 ) = 0

B = 5/3 units

L = 3( 5/3 ) + 4

L = 5 + 4 = 9 units

Hence, this is the required solution.

the first one is x^2+2x+2

the second one is x^2+4

the last one is x^2-4x+8