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. What is the area of the landscaper’s model?
area grows by the square of the linear scale.
That is because area = length*width
so, if each of length and width are 1/2 as big, the area is (1/2)(1/2) = (1/2)^2 as big.
So, the model is 1/4 the area of the enlarged patio.
my answer choices are 10 20 40 and 80 square feet this your answer dosnt answer my question
25
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To find the area of the landscaper's model, we need to work backwards from the given information.
We know that the enlarged patio has an area of 160 square feet, and it is an enlargement of the model patio. The scale factor between the enlarged patio and the model patio is 2.
Since the scale factor is 2, it means that the dimensions of the enlarged patio are twice as long as the dimensions of the model patio. To find the area of the model patio, we need to shrink the area of the enlarged patio by the square of the scale factor.
First, we calculate the side length of the enlarged patio by taking the square root of the area of the enlarged patio:
Side length of enlarged patio = sqrt(160) = 12.65 feet (rounded to two decimal places)
Since the dimensions of the model patio are half the size of the enlarged patio, we divide the side length of the enlarged patio by 2 to get the side length of the model patio:
Side length of model patio = 12.65 / 2 = 6.32 feet (rounded to two decimal places)
Now, we can calculate the area of the model patio by multiplying the length and width:
Area of model patio = 6.32 feet * 6.32 feet = 39.86 square feet (rounded to two decimal places)
Therefore, the area of the landscaper's model patio is approximately 39.86 square feet.