Square A has side lengths that are 166 times the side lengths of square B. The area of square A

Question

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 ?

Accepted Answer

The correct answer is 27,556 . The area of a square is s 2 , where s is the side length of the square. Let x represent the length of each side of square B. Substituting x for s in s 2 yields x 2 . It follows that the area of square B is x 2 . It&rsquo;s given that square A has side lengths that are 166 times the side lengths of square B. Since x represents the length of each side of square B, the length of each side of square A can be represented by the expression 166 x . It follows that the area of square A is 166 x 2 , or 27,556 x 2 . It&rsquo;s given that the area of square A is k times the area of square B. Since the area of square A is equal to 27,556 x 2 , and the area of square B is equal to x 2 , an equation representing the given statement is 27,556 x 2 = k x 2 . Since x represents the length of each side of square B, the value of x must be positive. Therefore, the value of x 2 is also positive, so it does not equal 0 . Dividing by x 2 on both sides of the equation 27,556 x 2 = k x 2 yields 27,556 = k . Therefore, the value of k is 27,556 .

Question 555b27