Problem 12, Anna looks at a photo on her smartphone. The format is 16 by 9 and fills the whole display. When she turns the smartphone, the picture gets smaller. What fraction of the display area is taken up by the smaller picture? So this is the picture originally filling the whole display, and then after we turn it, it's smaller, only fills up part of the display, but the format is still the same. And we're going to see that this used to be the width, right? This is the same length as this length here, but now it's the length of the picture. So this old width that we had is now the new length of the picture. And so because the photo fills up the whole display and it's 16 by 9, we know that the phone is also 16 by 9. So this tells us that the new length is 9 16ths of the old length, and that's because the old width here is 9 16ths of the old length, and this old width has become our new length. So our new length is 9 16ths of the old length, and this means that the new width is also 9 16ths of the old width. And so since the new length is equal to the old width, this means the new width is 9 16ths times 9 16ths, which is 81 out of 256 of the old length. Now, we know that originally we were taking up the whole display, and now we can still consider this width to be the same, but instead of this whole length here, we just have this portion, which we said was 81 over 256, out of the whole portion. And so that means that this rectangle is also going to be 81 over 256, the whole rectangle. And so the smaller picture takes up 81 over 256 of the display area, and the answer is E.

smartphone

16:9 display

image rotation

area ratio

screen format