Question

A rectangle has a length of 12 millimeters and a width of 17 millimeters.

What is the effect on the perimeter when the dimensions are multiplied by 12?


a. The perimeter is increased by a factor of 12.

b. The perimeter is increased by a factor of 48.

c. The perimeter is increased by a factor of 144.

d. The perimeter is increased by a factor of 576.

Answer 1

The perimeter is increased by a factor of 12.

Option (a) is correct .

Explanation:

Formula

Perimeter of a rectangle = 2 (Length + Breadth)

As given

A rectangle has a length of 12 millimeters and a width of 17 millimeters.

Perimeter of a rectangle = 2 × (12 + 17)

= 2 × 29

= 58 millimeters ²

As given

when the dimensions are multiplied by 12 .

New Length = 12 × 12

= 144 millimeter

New Breadth = 17 × 12

= 204 millimeter

Thus

New Perimeter of a rectangle = 2 × (144 + 204)

= 2 × 348

= 696 millimeter²

`(New\ perimeter\ of\ a\ rectangle)/(Perimeter\ of\ a\ rectangle) = (696)/(58)`

`(New\ perimeter\ of\ a\ rectangle)/(Perimeter\ of\ a\ rectangle) = 12`

Therefore the perimeter is increased by a factor of 12.

Option (a) is correct .

Answer 2

ok so original perimeter = 12 +12 + 17 +17 = 58 mm

if dimensions are multiplied by 12:

12*12 = 144 and 17*12 = 204

new perimeter = 144 +144 +204 +204 = 696 mm

696 / 58 = 12

so the perimeter increased by a factor of 12, answer is A