Question

noah drew a scaled copy of polygon p and labeled it polygon q. if the area of polygon p is 5 square units, what scale factor did noah apply to polygon p to create polygon q? scale factor:

Explanation:

Step1: Count the area of Polygon Q

Count the unit - squares in Polygon Q. There are 20 unit - squares, so the area of Polygon Q is 20 square units.

Step2: Use the area - scale factor relationship

The relationship between the areas of two similar polygons is $A_{2}=k^{2}A_{1}$, where $A_{2}$ is the area of the scaled polygon (Polygon Q), $A_{1}$ is the area of the original polygon (Polygon P), and $k$ is the scale factor. We know $A_{1} = 5$ and $A_{2}=20$. Substitute into the formula: $20=k^{2}\times5$.

Step3: Solve for the scale factor $k$

First, divide both sides of the equation $20 = k^{2}\times5$ by 5: $\frac{20}{5}=k^{2}$, so $k^{2}=4$. Then take the square root of both sides. Since the scale factor is positive (it represents a dilation), $k = 2$.

Answer:

2