<p>I tried looking this up, with no avail. I was doing SAT practice and a problem explained that if one side of a triangle is A, another is B, and the hypotenuse is C, then A+B must be less than 20.
Is there any minimum length requirement too? I know A+B has to be less than 20, but does it have to be more than something too? Like maybe the hypotenuse had to be more than A-B? The problem did not state there had to be any minimum requirement so idk.
Thanks a lot</p>
<p>A+B > C
A-B < C
and it goes for any other side too</p>
<p>In a nutshell:</p>
<p>A triangle has 3 sides. The theorem simply states that the sum of the 2 shorter sides has to be greater than the longest side (otherwise the triangle would be “open”). There is no “minimum” requirement. The only thing that needs to be satisfied is that the longest leg has to be shorter than the 2 other legs combined.</p>
<p>In the case of a right triangle, the sum of the lengths of the 2 legs has to be greater than the length of the hypotenuse.</p>
<p>^ true, but if you’re faced with a problem that goes along the lines of: “given a triangle with side lengths 3 and 7, what is the lowest and highest possible integer value for the third side”
then its better to think of the problem as a “max” and “min” requirement
and use the 7+3>C and 7-3<c, or=“” 10=“”>C and 4<C
thus “max” would be 9 and “min” would be 5</c,></p>
<p>wanago2college…</p>
<p>Perhaps something’s being lost in translation, but according to the question you posted, if the hypotenuse C in the question is 20, then actually the sum of A and B (the legs) must be greater than 20 (i.e., A + B > C, so A + B > 20), not less than 20.</p>
<p>If, on the other hand, the question says exactly what you wrote, then the only thing you can deduce is that the hypotenuse C MUST be less than 20 and here’s why…</p>
<p>You wrote that the question says the sum of the lengths of the legs A + B must be less than 20 (or, 20 > A + B), and we know that A + B > C (this is the rule…the sum of the lengths of any two sides of a triangle must be greater than the length of the third). So, 20 > A + B > C. It MUST be true, therefore, that 20 > C (or C < 20).</p>
<p>(This written explanation can be a bit confusing…hope it makes sense to you.)</p>
<p>In general, Selena’s got it pretty much nailed…</p>
<p>Basically, on the SAT, whenever you are given the lengths of two sides of any triangle and asked about possible values for the length of the third side, you should find the sum of and the difference between the two known sides…**the third side must be between these two values. **</p>
<p>For instance, if a question gives you a triangle with sides of length 3 and 7 (as in Selena’s example), you would know that the third side has to be between 4 (the difference) and 10 (the sum), not inclusive (i.e., the third side cannot be 4 or 10, only between.)</p>
<p>You may also get a question that requires you to work “backwards.” For instance, if they tell you that one side of the triangle is 8 and ask you something like “Which of the following could be the lengths of the other two sides?” you can still use this technique. Just find the sum of and difference between the values given in each answer choice and determine if 8 falls between the sum and difference.</p>
<p>Another variation…</p>
<p>A triangle’s sides have integer lengths. If one side has a length of 6 and another has a length of 9, what is the greatest possible length of the third side?</p>
<p>Again, find the sum and difference:
9 + 6 = 15
9 - 6 = 3
Greatest value for the third side would be 14.</p>
<p>Be careful, though… every now and then, ETS likes to try to trip students up on these questions by not specifying that you’re dealing with a triangle. For instance, suppose you are given that point A is 9 units from point B and point C is 5 units from point B, and you are asked about possible values for the distance from A to C. Well, if A, B, and C are arranged in a triangular fashion (they are “non-colinear,” or “not on the same line”), you can use the above technique to find the range of values for AC: 9 + 5 = 14 and 9 - 5 = 4. However, in this case, because ETS did not specify that the points lie in a triangle, AC could actually be 14 or 4 if the points lie on the same line. </p>
<p>A_____<strong><em>9</em></strong>__<strong><em>B</em></strong>5___C In this case, AC is 14.</p>
<p>A<strong><em>4</em></strong>C_<strong><em>5</em></strong>_B In this case, AC is 4.</p>
<p>Having said all of this, I know your question was a bit different, but hopefully some of this will help you on questions like it in the future.</p>