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 - side relationship for a square

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

Step2: Calculate the areas of square A and square B

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

Step3: Find the ratio of the areas

We know that $A_{A}=kA_{B}$. Substituting the expressions for $A_{A}$ and $A_{B}$, we get $166^{2}x^{2}=k\cdot x^{2}$. Since $x
eq0$ (a non - degenerate square has non - zero side - length), we can cancel out $x^{2}$ on both sides of the equation. So, $k = 166^{2}=27556$.

Answer:

$27556$