A rectangular photograph is twice as tall as it is wide. 1. A rectangular photograph is twice as tall as it is wide. When a 4 cm wide frame is placed around the photo, the area of the frame and photo equals three times that of the photo alone. The original width of the photograph alone is: a) 4 cm b) 6 cm c) 8 cm d) 10 cm e) 12 cm

You have a photograph that measures $w$ by $2w$, thus the area of the photograph is $2w^2$. The frame is 4cm wide which adds 4 cm on the left, top, bottom, and right. So the total frame measures $w+8$ by $2w+8$, with an area of $(w+8)(2w+8)$. We know the following equality:

$$(w+8)(2w+8)=3(2w^2)$$ $$2w^2+24w+64=6w^2$$ $$4w^2-24w-64=0$$ $$w^2-6w-16=0$$ $$(w-8)(w+2)=0$$

And the only positive solution is $w=8$ so the answer is c.

The answer is very similar to Martin's answer, however, he forgets to include the 4cm on both sides of the frame:


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4cm 4cm