Question

If the perimeter of a rectangle garden with a width of 15 is 125, what is the perimeter of the daily record it if the scale factor is 60%

Answer 1

(here i assume that the daily record is another rectangle)

For a rectangle with width W and length L, the perimeter is:

P = 2*W + 2*L

in this case we know that:

P = 125

W = 15

Replacing these in the perimeter equation we get:

125 = 2*15 + 2*L

125 = 30 + 2*L

125 - 30 = 2*L

95 = 2*L

95/2 = L = 47.5

Now we know that the daily record has a scale factor of 60%.

This means that each measure of this rectangle is (60%/100%) times the equivalent measure of the rectangle garden.

Then if the width of the daily record is W' and the length of the daily record is L'

This means that:

L' = (60%/100%)*L = 0.6*L = 0.6*47.5

W' = (60%/100%)*W = 0.6*W = 0.6*15

Then the perimeter is:

P' = 2*0.6*47.5 + 2*0.6*15 = 75

(notice that is exactly the same than multiplying the original perimeter by (60%/100%) = 0.6)