Blue Book Math Question

Test Preparation SAT Preparation
1

<p>Second edition, page 671, #16 - rectangle problem
"The pattern shown above is composed of rectangles. This pattern is used repeatedly to completely cover a rectangular region 12L units long and 10L units wide. How many rectangles of dimension L by W are needed."</p>

<p>The picture - you may want to look in the book - shows five rectangles. The first column shows two rectangles stacked vertically, the second shows three stacked horizontally. The width of each is W and the length of each is L.</p>

<p>Thus, I determined that 1.5W = L. I then divided 12L/1.5L = 8, so I knew that the end image is 8 patterns long. I next divided 10L/2L = 5L, so I knew that the end image is 2 patterns wide. Next, I multiplied 5 x 8 = 40, to get the total number of times the pattern is repeated. I then multiplied that by 5, because each pattern consists of 5 rectangles. I got 200. (I hope this makes sense, it's hard to describe.)</p>

<p>Collegeboard's answer if 180.
What did I do wrong and how did they do it right?</p>

<p>Thank you in advance.</p>

2

<p>Basically W=2/3 L. The rectangle they give you (composed of 5 rectangles) is then 2L by 1 and 2/3 L. 2L goes into 12L width 6 times and 1 and 2/3L goes in 6 times for the length. Multiply that by the 5 original rectangles for 180. (6<em>6</em>5)</p>

3

<p>I would start by picking values for L and W (make sure that you observe that 3W=2L; you can see this easily just by looking at the picture). The simplest such choice is L=3, W=2. Then just divide the whole area by the area of one rectangle:</p>

<p>(12<em>3</em>10*3)/6 = 180.</p>