The area of square A𝐴 is 625625 times the area of square B𝐵. Square A𝐴 has side lengths that are k𝑘 times the side lengths of square B𝐵. What is the value of k𝑘?
Question
The area of square A𝐴 is 625625 times the area of square B𝐵. Square A𝐴 has side lengths that are k𝑘 times the side lengths of square B𝐵. What is the value of k𝑘?
Solution
The area of a square is calculated by squaring the length of one of its sides. If square A has an area that is 625 times the area of square B, and the side lengths of square A are k times the side lengths of square B, we can set up the following equation:
(k * side length of B)^2 = 625 * (side length of B)^2
Solving for k, we get:
k^2 = 625
Taking the square root of both sides, we find:
k = 25
So, the side lengths of square A are 25 times the side lengths of square B.
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