Question

A rectangular garden has a fence around it with perimeter P. If the width of the garden isincreased by n units, describe the new perimeter in terms of Pand n.

Answer 1

The perimeter of a rectangle

If a rectangle has a width W and length L, the perimeter is the sum of all 4 sides:

P=2W+2L

The rectangular garden has a fence around it and we know the value of P, it is considered as a data.

Now we are told the width of the garden is increased by n units. It means the new width is W2=W+n. Assume the length is not changed.

The new perimeter is:

P2=2(W+n)+2L

Operating:

P2=2W+2n+2L

Rearranging:

P2=2W+2L+2n

Note the bold part is equal to the original perimeter P, thus:

P2=P+2n