A model of a rectangular patio at a landscaping business will be enlarged by a scale factor of 2 when it is installed in a customer’s back yard. The area of the new enlarged patio will be 160 square feet. Which is the area of the landscaper’s model?

10 square feet
20 square feet
40 square feet
80 square feet

it is 40 square feet

idk bc i need the answer

To find the area of the landscaper's model, we need to use the concept of scale factor.

Given that the new enlarged patio has an area of 160 square feet and is created by scaling up the landscaper's model by a scale factor of 2, we can set up the equation:

Area of the enlarged patio = Scale factor^2 × Area of the landscaper's model

Plugging in the given values, we have:

160 = 2^2 × Area of the landscaper's model

Simplifying the equation, we get:

160 = 4 × Area of the landscaper's model

Dividing both sides of the equation by 4, we have:

40 = Area of the landscaper's model

Therefore, the area of the landscaper's model is 40 square feet.

So, the correct answer is 40 square feet.

if A = LW then the new area

A' = (2L)(2W) = 4LW = 4A

so, 4A = 160