A rectangle has a width of 3 cm and a length of 10 cm.What is the effect on the perimeter when the dimensions are multiplied by 10? The perimeter is increased by a factor of 10. The perimeter is increased by a factor of 40. The perimeter is increased by a factor of 100. The perimeter is increased by a factor of 400.

To know the factor that affect the perimeter, we should know the former perimeter and the new perimeter after the dimension change. Then compare them both.

First, determine the perimeter of the former dimension
p = 2 (l + w)
p = 2 (3 + 10)
p = 2 (13)
p = 26 cm

Second, determine the new dimension
l₁ = 10l
l₁ = 10(10)
l₁ = 100 cm

w₁ = 10w
w₁ = 10(3)
w₁ = 30 cm

Third, determine the new perimeter
p₁ = 2(l₁ + w₁)
p₁ = 2(100 + 30)
p₁ = 2 (130)
p₁ = 260 cm

Last, compare the former perimeter to the new perimeter
p : p₁ = 26 : 260
p₁ = 10p
the new perimeter is increased by a factor 10

The answer is first option