Scale factor, Price per meter

Question

A rectangular display, with the dimensions 3m by 4m, shows the layout for Trout River conservation area. The display was created using a scale of 1:150.

It costs the state $0.65m² to maintain Trout River from spring through fall. What is the approximate cost to maintain the conservation area?

Answer 1

Hi Scott,

Since it asks for cost to maintain the conservation area, we need to find its area. We do this using the scale factor.

Scale factor typically refers to scaling of the sides. Because ours is 1:150, that means that the length of both sides of the conservation area is 150 times the length of the sides of the display. So we do:

3 x 150 = 450

4 x 150 = 600

So the dimensions of the conservation area are 450 m x 600 m. Multiplying, we get a conservation area of 270,000 square meters. At $0.65 per square meter, the total cost would be $175,500.

Hope that helps.