Question

State if the statement is true or false

If the length of a rectangle is halved and breadth is doubled, then the area of the rectangle obtained remains same.

Answer 1

Let the length of a rectangle be $l$
Let the length of a rectangle be $b$
$\Rightarrow$ Area of rectangle $=lb$---(1)

New length of rectangle, $\left(L\right)=\frac{l}{2}$
New breadth of rectangle, $\left(B\right)=2b$

$\Rightarrow$ Area of new rectangle $=\frac{l}{2}\times 2b=l\times b=lb$---(2)

From (1) and (2),

Area of rectangle $=$ Area of new rectangle.

Therefore, If the length of a rectangle is halved and breadth is doubled, then the area of the rectangle obtained remains same.