Question

Describe how to find the perimeter of an enlarged figure if you know the scale factor and the dimensions of the original figure.

Answer 1

Perimeter of any figure is given by adding up all the side measurements.

So, when a figure is enlarged by a scale factor then we can multiply all the sides with the scale factor to get the new sides measurements and then we can find the perimeter.

Or simply we can find the perimeter of the original figure and then multiply by the scale factor.

In both the methods, the answer will be the same.

We can take an example:

Lets suppose the original figure to be a rectangle with length 5 cm and width 2 cm. The rectangle is enlarged by a scale factor of 6.

The original perimeter is =
`2(5+2)`

=
`2(7)=14` cm

1st method:

Multiply the length by 6 and width by 6 to get new dimensions.

Length becomes:
`5*6=30`

Width becomes:
`2*6=12`

Perimeter becomes:
`2(30+12)`

=
`2(42)=84` cm

2nd method:

Simply multiply 6 with the original perimeter.

`14*6=84` cm

We can see that in both methods, the perimeter is same.