Question

jacob designs a building with a square base. he starts by building a model for the building, which has a base with an area of 36 feet². the base of the real building will have an area of 6084 ft.². what is the scale factor between the model and the real building? 169 6 78 13

Explanation:

Step1: Recall the relationship between area - scale factor

The ratio of the areas of two similar figures is equal to the square of the scale factor. Let the scale factor be $k$. If $A_1$ is the area of the model and $A_2$ is the area of the real - building, then $\frac{A_2}{A_1}=k^{2}$.

Step2: Identify the areas

We are given that $A_1 = 36$ square feet (area of the model) and $A_2=6084$ square feet (area of the real - building).

Step3: Calculate the square of the scale factor

$k^{2}=\frac{A_2}{A_1}=\frac{6084}{36}=169$.

Step4: Find the scale factor

Take the square root of both sides. Since $k>0$ (scale factor is a positive quantity), $k = \sqrt{169}=13$.

Answer:

13