The perimeter of a rectangle becomes __________ times its original perimeter, if its length and breadth are doubled.

Solution:

If L = length of the rectangle and

B = breadth

Therefore the perimeter of the rectangle P, is = 2(L + B) — (1)

If the length is doubled to 2L and

If the breadth is doubled to 2B then

The perimeter P’ will be

P’ = 2(2L + 2B)

P’ = 4(L + B)

We know from (1) that P = 2(L + B)

Therefore

P’ = 2[2(L + B)]

P’ = 2P

Hence the new perimeter is twice that of the original perimeter.

✦ Try This: The perimeter of a rectangle becomes __________ times its original perimeter, if its length and breadth are halved.

If L = length of the rectangle and

B = breadth

Therefore the perimeter of the rectangle P, is = 2(L + B) — (1)

If the length is halved to L/2 and

If the breadth is halved B/2 then

The perimeter P’ will be

P’ = 2(L/2 + B/2)

P’ = (L + B) (2)

We know from (2) that

P’ = (L + B)

Therefore

P’ = 1/2 × [2(L + B)]

P’ = 1/2 × P

The perimeter of a rectangle becomes 0.5 times its original perimeter, if its length and breadth are halved.

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 11

NCERT Exemplar Class 8 Maths Chapter 11 Problem 39

Summary:

The perimeter of a rectangle becomes two times its original perimeter, if its length and breadth are doubled

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