Question

if the length of a rectangle becomes half and breadth of a rectangle becomes doubled then the area of the rectangle is what?
1. becomes 1/4th
2. remains same
3. becomes doubled
4. becomes 4 times. ​

Answer 1

Step-by-step explanation:

Given -

• Length of the rectangle becomes half
• Breadth of the rectangle becomes doubled

To Find -

• Area of the rectangle is what ?

Let x be the length of the rectangle

and

y be the breadth of the rectangle

Then, New length = x/2

Then, The breadth is 2y

As we know that :-

• Area of rectangle = l × b

→ Area of rectangle = xy

And

New Area of rectangle :-

→ Area = x/2 × 2y

→ Area = xy

Hence,

The area of the rectangle remains same.

Therefore, Option (2) is correct.

Additional information :-

• Area of rectangle = l × b
• Perimeter = 2(l + b)
• Each angle of rectangle is of 90°
• Opposite sides of rectangle are equal.

Answer 2

GIVEN :–

• Length of a rectangle becomes half .

• Breadth of a rectangle becomes doubled.

TO FIND :–

• New area of rectangle = ?

SOLUTION :–

▪︎ Let the length of rectangle is 'x' and breadth is 'y'.

▪︎ According to the question –

• New length = x/2

• New breadth = 2y

▪︎ We know that –

• Area of rectangle = length × breadth

⇒ Area of rectangle = xy

▪︎ Now let's find new area –

⇒ New area = (New Length) × (New breadth)

⇒ New area = (x/2) × (2y)

⇒ New area = xy

⮕ Area remains same.

Hence , Option (2) is correct.

Additional information :–

(1) Area of rectangle = (Length × breadth)

(2) Perimeter of rectangle = 2[ Length + breadth ]