If length of a rectangle is halved and breadth is doubled then the area of the rectangle obtained remains same.
Step 1: Recall the area formula.
Area of a rectangle = length × breadth.
So, original area: ( A_{ ext{old}} = l imes b ).
Step 2: Change the sides as given.
New length = ( frac{l}{2} ).
New breadth = ( 2b ).
Step 3: Write the new area.
( A_{ ext{new}} = left( frac{l}{2} ight) imes (2b) ).
Step 4: Multiply step by step.
( frac{l}{2} imes 2 = l ).
So, ( A_{ ext{new}} = l imes b ).
Step 5: Compare with the original area.
( A_{ ext{new}} = A_{ ext{old}} ).
Therefore, the area stays the same. The statement is true.
Quick number check (to build confidence):
Let ( l = 10 ) and ( b = 3 ).
Original area: ( 10 imes 3 = 30 ).
New length: ( frac{10}{2} = 5 ). New breadth: ( 2 imes 3 = 6 ).
New area: ( 5 imes 6 = 30 ). Same as before.