Question

area of rectangle is X ² + 12 X Y + 27 y ² and its length is (X +9 y) find the breadth of rectangle

Answer 1

here.
area of rectangle is given =x²+12xy+27y²
Length of rectangle =x+9y
then area of rectangle =length x breadth
x²+12xy+27y² =x+9y x breadth

X²+9xy+3xy+27y² =x+9y x breadth
x(x+9y)+3y(x+9y) =x+9y x breadth
(x+3y) (x+9y) =x+9y x breadth
breadth = x+3y anwer

Answer 2

Answer:

Breadth of the rectangle = (x +3y)  

Step-by-step explanation:

Given area of the rectangle = x² + 12xy +27 y²

given that length of the rectangle = (x + 9y)

As we know that area of the rectangle = length × breadth

from given data (x + 9y) × breadth = x² + 12xy +27 y²                            

        (x + 9y) × breadth = x² +9xy + 3xy+27 y²    [  12xy = 9xy +3xy ]  

        (x + 9y) × breadth = x² +9xy + 3xy+27 y²      

        (x + 9y) × breadth = x(x +9y) + 3y (x+9y)     [ take x and 3y common ]

        (x + 9y) × breadth = (x +9y)  (x +3y)              [ take (x +9y) common ]  

⇒ breadth = (x +3y)