Question

Tawney is designing a playground in the shape of a rectangle. If Tawney increases the length and width of the playground by a scale factor of 3, what will be the resulting effect on the perimeter of the new playground?

Answer 1

When Tawney increases the length and width of the playground by a scale factor of 3, the perimeter of the playground will also increase by a factor of 3.

Step-by-step explanation:

If Tawney increases the length and width of a rectangular playground by a scale factor of 3, the perimeter of the new playground would increase by a factor of 3 as well. To understand why, consider that the perimeter of a rectangle is the sum of all its sides, or 2 × (length + width). By multiplying both the length and width by 3, you are effectively tripling the total length of the two longer sides and the two shorter sides. So, if the original perimeter is represented by 2l + 2w (where l is the original length and w is the original width), the new perimeter would be 2 ×(3l) + 2 ×(3w) = 6l + 6w, which is three times the original perimeter.