Question

The perimeter of the square is 48m. The area of the rectangle is 4sq.m less than the area of the given square. If the length of rectangle is 10m, then its breadth is equal to
A) 8m
B) 9m
C) 10.5m
D) 10m

Answer 1

Hint:
Given perimeter of square by that we will find the side of the square and then the area of the square, again area of rectangle is 4sq.m less than the area of given square by that we will find area of rectangle, and lastly length of rectangle is given by which we will find the breadth of rectangle.

Complete step by step solution:

The perimeter of square is given by the formula:
 $perimeter(p) = 4 \times side$
As the perimeter of square is 48m
 $ \Rightarrow 48m = 4 \times side$
On dividing the equation by 4 we get,
 $ \Rightarrow side = 12m$
Now the area of square is given by
 $Area = {(side)^2}$
As the side length is 12m
 $ \Rightarrow Area = {(12m)^2} = 144sq.m$
Since the area of rectangle is 4sq.m less than the area of square
Therefore, the area of rectangle =144sq.m-4sq.m=140sq.m
Lastly the area of rectangle is given by the formula
 $Area = (l \times b)$
As the length ‘l’ is given as 14m
 $ \Rightarrow 140sq.m = (14m \times b)$
On dividing the equation by 14 we get,
 $ \Rightarrow b = 10m$
So, the breadth of rectangle is 10m

Therefore option ‘D’ is correct.

Note:
Perimeter of square is given by $perimeter(p) = 4 \times side$ (That is $4 \times $ its side length)
Area of square is given by $Area = {(side)^2}$ (That is side $ \times $ side)
Area of rectangle is given by $Area = (l \times b)$ (Where ‘l’ and ‘b’ are length and breadth of rectangle)
Perimeter of rectangle is given by $perimeter(p) = 2(l + b)$ (Where ‘l’ and ‘b’ are length and breadth of rectangle)