which of the following inequalities indicates the set of all values of d for which the lengths W of the three sides of a triangle can be 3,4, and d?  Choose the correct choice from the following answers
A) 0<d<1 B) 0<d<5 C) 0<d<7 D) 1<d<5 E) 1<d<7
This question is a good way to apply one of the most basic relation between the 3 sides of a triangle. In a triangle (ANY TRIANGLE), any side MUST be greater than the positive difference of the other two sides and less than than the sum of the other 2 sides. Let the sides of a triangle be a,b,c .   Thus,   |a-b| &lt; c &lt; a+b   |b-c| &lt; a &lt; b+c   |c-a| &lt; b &lt; a+c   Thus, if the sides of the triangle are 3,4 and d,   4-3<d<4+3 ---=""> 1&lt;d&lt;7. Thus 1&lt;d&lt;7 is the correct answer.</d<4+3>
<result>E</result>
which of the following inequalities indicates the set of all values of d for which the lengths W of the three sides of a triangle can be 3,4, and d?