<p>Need help for 2 problems in the College Board's new SAT I Official Study Guide
(the book with 8 practice tests).
both are geometry Q's & thanks in advance for any help!!</p>
<p>p. 721, #16: I can get the answer but that's contigent on the
4 triangles (inside the 3x3 square) being congruent.
But why are they congruent??</p>
<p>p.738, #20 - Is this problem worded incorrectly?
there could be more than 1 answers, not just the (b) choice given in the book?
Reason being "length+width = 8" can have multiple pairings such as
l=5, w=3, l=4.5, w=3.5, ...?
i.e. l/w need not be integers only?</p>
<p>Well, well ... no answers from the current crop of test takers :)</p>
<p>Anyway, I'll put you on the right track without solving it completely.</p>
<p>When reading a problem, you have to pay attention to ALL the clues given. For instance, your first question stated that the inscribed figure is a square. Then the larger figure does have 3 right angles, resulting that it also had to be a square and have 4 90 degree angles. What do you have now? The small triangles all have an identical hypothenuse and are right triangles. What does that tell you? The rest is easy. </p>
<p>For your second problem, you need to see that there are 5 answers that all seem pretty simple. This is a good indicator that the question will be simple but require a bit of logic. This is not a calculator question -very few are, for that matter. Again, what is the clue that you cannot miss here: one of the inscribed figure is a RECTANGLE. What do we know about the diagonals of a rectangle? They are equal. Draw the second diagonal ... oops a bit of magic, and what does it become: just another radius and its value is 6. FWIW, just notice that any other rectangle built in a similar way will ALWAYS have the same diagonal,</p>
<p>Anyhow, now that you have the diagonal at 6, it a simple calculation to to plug in the numbers for the quarter circumference, and the numbers 6 and 8 in the right order. Piece of cake. </p>
<p>The lesson here. If you seem to be stuck on a problem, read it again and look for any clues that you have overlooked.</p>
<p>Wow, that's great explanations - so clear & helpful.
And it's super that you didn't just go ahead & solve the whole thing in a few quickie steps but pointed out what to think about.
Thanks very very much!!!</p>
<p>I've worked through the entire new CB book for math and those were the last 2 stumbling blocks ...
but I'm sure on a real test, CB can still have plenty of surprises in their problem bank! Sigh!</p>
<p>Hmmm. I thought that all figures on the SAT I were drawn to scale, unless otherwise noted. If that is the case, CT = 3 and SA = 1, just by eye-balling it and using common sense [since we know that the perimeter = 3pi + 6 + (SA + CT)]. Using those numbers as guides for the pythagorean theorem for the the triangle ARC, RA does not = 5, or RC does not = 3. I must be missing a geometry concept...please fill me in! Thanks.</p>
<p>Setzxman:
I think your eyeballing is a bit off and the drawing is probably slightly off scale (at least horizontally). Via eyeballing, you concluded: CT = 3 and SA = 1. If you measure the drawing with enough precision, I think you can see that SA is indeed less than 1, making RA greater than 5 (and RC less than 3). Of course, eyeballing (or measuring) doesn't make sense when there is a straightforward math approach to the probelm. If you can't see the math principles right away, then of course, use eyeballing. In this case, you'd get the right answer, even with the wrong measured guesstimates for the sides.</p>