Question

the dimensions of a rectangle are(8x+6y)and (4x+2y)meters .if a path of uniform width (x+y)metersruns all around on the outside then the area of the path is​

Answer 1

Answer:

Area of path = 13x² + 22xy + 9y²

Step-by-step explanation:

length of rectangle = 8x + 6y

breadth of rectangle = 4x + 2y

area of rectangle = length × breadth

= (8x + 6y) × (4x + 2y)

= 32x² + 16xy + 24xy + 12y²

= 32x² + 40xy + 12y²

width of path = x + y

length of rectangle with path

= 8x + 6y + x + y

= 9x + 7y

breadth of rectangle with path

= 4x + 2y + x + y

= 5x + 3y

area of rectangle with path

= (9x + 7y) × (5x + 3y)

= 45x² + 27xy + 35xy + 21y²

= 45x² + 62xy + 21y²

area of path = area with path - area without path

(45x² + 62xy + 21y²) - (32x² + 40xy + 12y² )

= 45x² + 62xy + 21y² - 32x² - 40xy - 12y²

= 13x² + 22xy + 9y²

Hope you get your answer