Question

A rectangle has a width of 12.5 m and a length of 105 m. What is the effect on the perimeter when the dimensions are multiplied by 2?

Answer 1

P=2(L+W)
when we double each
Pnew=2(2L+2W)
Pnew=2(2(L+W))
Pnew=2(P)
the perimiter is doubled

if you wanted the actual perimiter
P=2(L+W)
P=2(12.5+105)
P=2(117.5)
P=235 m
double it to get
470m is the doubled perimiter

Answer 2

For this case we have that by definition, the perimeter of a rectangle is given by:

`P = 2 (w + l)`

Where,

• w: width of the rectangle
• l: length of the rectangle

The original perimeter is given by:

`P1 = 2 (12.5 + 105)\\P1 = 235`

Then, the new perimeter is given by:

`P2 = 2 ((2 * 12.5) + (2 * 105))\\P2 = 2 * 2 (12.5 + 105)\\P2 = 2 * 235\\P2 = 2 * P1`

Therefore, the original perimeter increases by a factor of 2.

Answer:

the original perimeter increases by a factor of 2.

`P2 = 2 * P1`