2006 CEMC Pascal Problems/Problem 8

Problem

The areas of three squares are $16$ , $49$ and $169$ . What is the average (mean) of their side lengths?

$\text{ (A) }\ 8 \qquad\text{ (B) }\ 12 \qquad\text{ (C) }\ 24 \qquad\text{ (D) }\ 39 \qquad\text{ (E) }\ 32$

Solution

The side length of a square is also equivalent to the square root of its area. This means that we can simply find the side lengths of all the squares using the area, and then take the average.

The first square with an area of $16$ has a side length of $\sqrt{16} = 4$ .

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The second square with an area of $49$ has a side length of $\sqrt{49} = 7$ .

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The last square with an area of $169$ has a side length of $\sqrt{169} = 13$ .

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Taking the average of their side lengths, we get $\frac{4 + 7 + 13}{3} = \frac{11 + 13}{3} = \frac{24}{3} = \boxed {\textbf {(A)} 8}$

~anabel.disher

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2006 CEMC Pascal Problems/Problem 8

Problem

Solution