2000 CEMC Gauss (Grade 8) Problems/Problem 15

Problem

$ABCD$ is a square that is made up of two identical rectangles and two squares of area $4$ $\text{cm}^{2}$ and $16$ $\text{cm}^{2}$ . What is the area, in $\text{cm}^{2}$ , of the square $ABCD$ ?

$\text{ (A) }\ 64 \qquad\text{ (B) }\ 49 \qquad\text{ (C) }\ 25 \qquad\text{ (D) }\ 36 \qquad\text{ (E) }\ 20$

Solution

First, we can draw a diagram to make the problem easier to visualize.

An image is supposed to go here. You can help us out by creating one and editing it in. Thanks.

We can find the side lengths of the squares because the side lengths are just the square roots of their areas. We then have:

$\sqrt{4} = 2$ $\text{cm}$

$\sqrt{16} = 4$ $\text{cm}$

An image is supposed to go here. You can help us out by creating one and editing it in. Thanks.

We can now see that the side length of $ABCD$ is just the sum of the side lengths of the smaller squares. Thus, the side length is $2 + 4 = 6$ $\text{cm}$ .

From the side length, $[ABCD] = 6^2 = \boxed {\textbf {(D) } 36}$ $\text{cm}^{2}$ .

~anabel.disher

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2000 CEMC Gauss (Grade 8) Problems/Problem 15

Problem

Solution