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ABCD is a square picture frame (see figure). EFGH is a

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by BTGmoderatorDC » Sun Aug 26, 2018 5:27 pm
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ABCD is a square picture frame (see figure). EFGH is a square inscribed within ABCD as a space for a picure. The area of EFGH (for the picture) is equal to the area of the picture frame (the area of ABCD minus the area of EFGH). If AB = 6, what is the length of EF?

$$A.\ 3\sqrt{3}$$
$$B.\ 4\sqrt{2}$$
$$C.\ 5\sqrt{3}$$
$$D.\ 3\sqrt{2}$$
$$E.\ 2\sqrt{5}$$

OA D

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by ceilidh.erickson » Mon Aug 27, 2018 11:44 am
If the length AB = 6, then the area of the entire figure (frame + picture) = 36.

Since the frame and picture both have an equal area, the area of each must be 18.

If square EFGH has an area of 18, then each side length must be: $$\sqrt{18}$$
$$=3\sqrt{2}$$
The answer is D.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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