Question

The area of a rectangular field is 25x2 + 20xy + 3y2 square unit. If its length is 5x + 3y unit, find its breadth, Hence find its perimeter.

Answer 1

Area of a rectangle

= 25x² + 20xy + 3y² 

Length = (5x + 3y) units

∴ Breadth = `"Area"/"Length"`

`= ("25x"^2 - 20"xy" + 3"y"^2)/"5x + 3y"`

                 5x + y
`"5x" + "3y")overline(25"x"^2 + 20"xy" + 3"y"^2)(`
               25x² + 15xy 
              -       -             
              5xy + 3y²
              5xy + 3y²  
             -       -        
                 xxx         

Hence Breadth = 5x + y

Hence perimeter of rectangular field

= 2 (l + b)

= 2 (5x + 3y + 5x + y)

= 2 (10x + 4y)

= 20x + 8y