2000 CEMC Pascal Problems/Problem 7

Problem

Three squares with the same centre and corresponding parallel sides are drawn. The distance between the sides of successive squares is $3$ and the side length of the largest square is $22$ , as shown. What is the perimeter of the smallest square?

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$\text{ (A) }\ 40 \qquad\text{ (B) }\ 100 \qquad\text{ (C) }\ 10 \qquad\text{ (D) }\ 64 \qquad\text{ (E) }\ 20$

Solution

To find the perimeter of the square, we can find the side length of the small square, and then multiply it by $4$ .

Let $s$ be the side length of the small square. We also know that distance between the sides of successive squares is $3$ .

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We can see that the side length of the full square is then $s + 3 \times 4$ , allowing us to set up an equation:

$s + 3 \times 4 = 22$

$s + 12 = 22$

$s = 10$

Multiplying this by $4$ to get the perimeter, we get $\boxed {\textbf {(A) } 40}$ .

~anabel.disher

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2000 CEMC Pascal Problems/Problem 7

Problem

Solution