Question

15 mark for review square a has side lengths that are 166 times the side lengths of square b. the area of square a is k times the area of square b. what is the value of k?

Explanation:

Step1: Recall the area formula for a square

The area formula of a square is $A = s^{2}$, where $s$ is the side - length. Let the side - length of square B be $s_{B}$, then the side - length of square A is $s_{A}=166s_{B}$.

Step2: Calculate the areas of square A and square B

The area of square B, $A_{B}=s_{B}^{2}$. The area of square A, $A_{A}=s_{A}^{2}=(166s_{B})^{2}$.

Step3: Expand the expression for the area of square A

Using the power - of - a - product rule $(ab)^{n}=a^{n}b^{n}$, we have $(166s_{B})^{2}=166^{2}s_{B}^{2}=27556s_{B}^{2}$.

Step4: Find the ratio of the areas

We know that $A_{A}=kA_{B}$. Since $A_{A}=27556s_{B}^{2}$ and $A_{B}=s_{B}^{2}$, then $k = 27556$.

Answer:

27556