Question

The length of a rectangle is 1 cm more than its breadth A square of side 'p' has been cut out of it If 'p' is one third the breadth of the rectangle the remaining area is
A. \[(8{p^2} + 3p)\;\] $cm^2$
B. \[(3{p^2} + 8p)\;\] $cm^2$
C. \[(8{p^2} + 8)\;\] $cm^2$
D. \[(3{p^2} + 8)\;\] $cm^2$

Answer 1

Hint: The remaining area of the rectangle can be calculated by firstly calculating the calculating the area of the rectangle in terms of p then finding the area of the square then subtract the area of the square to the area of the rectangle. To know the side length of the rectangle or the square just follow the given condition in the question like the length of the rectangle is 1 more than the breadth of the rectangle.

Complete step-by-step answer:
Given that the side of square is p cm and P is one third of breath of rectangle and length is 1 cm more the breadth rectangle
Suppose the side of the square is ‘p’cm
Then breadth of the rectangle \[ = 3p\] and length of the rectangle \[ = 3p + 1\]
As mentioned in the question that length is 1 more than the breadth.
We know the area of the rectangle is length times breadth
So the area of rectangle \[ = 3p\left( {3p + 1} \right)\]
 \[ = 9{p^2} + 3p\]
If a square of side p cut into rectangle
As we know the area of the square is square of the side length
Then the area of square \[ = {p^2}\]
So Remaining area left of rectangle after cutting of square= area of the rectangle – area of the square
 \[ = 9{p^2} + 3p - {p^2}\]
Or,
 \[ = (3{p^2} + 8)\;\] $cm^2$
So, the correct answer is “Option A”.

Note: Here in this question students do not let the length or breadth of the rectangle anything as in the question it has mentioned that the breadth of the rectangle should be 3 times of the side length of the square. So proceed from the square not from the rectangle as it is given that the side length of the square is ‘p’.