Distance SAT problem

Test Preparation SAT Preparation
1

<p>The distance form Town A to Town B is 5 miles and the distance from town B to town C is 4 miles. Which of the following could NOT be the distance from town A to Town C?</p>

<p>(A) 1
(B) 4
(C) 8
(D) 9
(E) 10</p>

<p>The correct answer is E but this means that B and C could be the distance from town A to town C. How can these be the distance? I tried all the combinations (ABC, BCA, ACB) and could only get 1 and 9</p>

2

<p>This is a standard “triangle rule” problem. A, B and C form a triangle, except in the extreme cases where they form a line.</p>

<p>The triangle rule says that the third side of a triangle is strictly between the difference and sum of the other two sides. In this case the difference is 1 and the sum is 9. So the third side of the triangle is between 1 and 9. But in this problem, a straight line is also okay. So the only number that doesn’t work is 10, choice (E).</p>

3

<p>Commonly known as the Triangle Inequality Theorem, here is some info on it for future reference: <a href=“Triangle inequality theorem- Math Open Reference”>http://www.mathopenref.com/triangleinequality.html&lt;/a&gt;. Basically, it states that if there is a triangle with sides a, b and c, three inequalities are satisfied:</p>

<p>a+b > c
b+c > a
a+c > b</p>

<p>Practice other problems like this one in order to ensure mastery of the topic.</p>

4

<p>Place A and B on a line separated by 5 units, and from B draw a circle with a radius of 4. This will show you all the possible answers. </p>

<p>The straight line approach is still the simplest. </p>

5

<p>If you’ve ever watched this show as a kid… you would’ve never realized it taught triangle side inequality concepts. </p>

<p><a href=“Cyberchase 204 True Colors part 2 - YouTube”>Cyberchase 204 True Colors part 2 - YouTube;

<p>The end of the video visualizes the theorem perfectly. </p>

6

<p>A visual reminder of why the teaching of math sucks so badly in the US. Cartoons, gimmicks, and other silly devices will never mask the lack of competent teachers. </p>

7

<p>Thanks guys!</p>

8

<p>“A visual reminder of why the teaching of math sucks so badly in the US. Cartoons, gimmicks, and other silly devices will never mask the lack of competent teachers.”</p>

<p>@xiggi I agree 100%. </p>