math help!

Test Preparation SAT Preparation
1

<p>1) in triangle PQR the length of side QR is 12 and the lenth of side PR is 20. What is the greatest possible integer length of side PQ.
a)9
b)16
c)25
d)27
e)31
The answer is E, I got 16... not sure how to attack this</p>

2

<p>I answer is E because according to the triangle inequality rule, the sum of any two sides of a triangle must be greater than the remaining side.</p>

<p>That is my reasoning on this, i’ve seen a problem similar to this and i got it right based on that.</p>

3

<p>They never specify that it is a right triangle or any other special triangle. So your only limitation is that the third side must be shorter than the sum of the other two sides, or in this case, less than 32. Since they limited us to integers, that means that the biggest possible value is 31.</p>

<p>The key fact, that the two shorter sides of a triangle must always add up to MORE than the third side, is one of the simplest yet most easily overlooked little ideas they test on the SAT.</p>

4

<p>If you add 12 and 20 together you get 32. The third side can’t be 32 because that would just be a straight line. Thus, you look at the criterion of integers, and find the integer below 32. Oh guess what? 31 is an answer choice! :D</p>

5

<p>20+12=32 no side must be greater than that
so side PQ < 32</p>

<p>E</p>

<p>Thanks for the refresher! the SAT uses the triangle inequality a lot on the harder questions in my short experience taking it. good luck this fall if you are taking it the same time I am that is</p>

6

<p>this is the second time I have forgot about this lol… These are the things stopping me from a perfect score… :(</p>

7

<p>In triangle PQR, if QR = 12 why PR = 20. There is a simple rule to attack these types of “triangle length questions.”

  1. Take the difference of both sides. 20 - 12 = 8
  2. Find the sum of both sides. 20+12 = 32
  3. Set up an inequality between the two new values. 8 < PQ < 32.</p>

<p>It is < and not less than or equal to. Therefore, now you have a clear range of possible values for PQ. If 32 were a choice, it would be WRONG because if PQ was 32 that would mean one angle in the triangle is 0 degrees (therefore no longer a triangle). So 1 below it is possible. </p>

<p>~Aceventura74</p>