+0  
 
0
115
1
avatar

In quadrilateral ABCD, we have AB = 3, BC = 6, CD = \(9\), and DA = \(12\).
If the length of diagonal AC is an integer, what are all the possible values for AC? Explain your answer in complete sentences.

 May 13, 2022
 #1
avatar+9461 
0

Triangle inequality implies \(\begin{cases} 3 + 6 > AC\\ 3 + AC > 6\\ 6 + AC > 3\\ 9 + AC > 12\\ 9 + 12 > AC\\ 12 + AC > 9 \end{cases}\). If you list the integers satisfying all 6 inequalities, the possible values would be 4, 5, 6, 7, 8.

 May 14, 2022

11 Online Users