Question

if we increase the length by 2 units and the breadth by 2 units, then the area of rectangle is increased by 54 square units. find the perimeter of the rectangle (in units)

Answer 1

Let the original length of the rectangle be L units and the original breadth be B units.

The area of the rectangle is given by: Area = L * B If we increase the length by 2 units, the new length will be (L + 2) units.

Similarly, if we increase the breadth by 2 units, the new breadth will be (B + 2) units.

The new area of the rectangle will be: New Area = (L + 2) * (B + 2)

According to the given information, the new area is increased by 54 square units:

New Area - Area = 54 Substituting the expressions for New Area and Area: (L + 2) * (B + 2) - L * B = 54

Expanding the expressions: LB + 2L + 2B + 4 - LB = 54

Simplifying: 2L + 2B + 4 = 54

Subtracting 4 from both sides: 2L + 2B = 50

Dividing both sides by 2: L + B = 25

Now, the perimeter of the rectangle is given by: Perimeter = 2 * (L + B)

Substituting the value we obtained earlier: Perimeter = 2 * 25 = 50 units

Hence, the perimeter of the rectangle is 50 units, which corresponds to option A) 50.