+14 In quadrilateral ABCD, we have AB = 3, BC = 6, CD = 4, and DA = 4.
If the length of diagonal AC is an integer, what are all the possible values for AC? Explain your answer in complete sentences.
+4622 Notice that AC splits the quadrilateral into two pieces.
ABC is a triangle as well as ADC.
By the Triangle Inequality for triangle ABC, AC must be greater than 6-3=3 and less than 6+3=9. The values are between 4 and 8, inclusive.
By the Triangle Inequaliyt for triangle ADC, AC must be greater than 4-4=0 and less than 4+4=8. The values are between 1 and 7, inclusive.
Thus, the values in the intersection between the two inequalities are from 4-7 for 7-4+1=4 values that satisfy AC, namely 4, 5, 6, and 7 units.
+14 sorry, i'm kinda new to this whole thing and I realized that I did that on accident :(
Notice that AC splits the quadrilateral into two pieces.
ABC is a triangle as well as ADC.
By the Triangle Inequality for triangle ABC, AC must be greater than 6-3=3 and less than 6+3=9. The values are between 4 and 8, inclusive.
By the Triangle Inequaliyt for triangle ADC, AC must be greater than 4-4=0 and less than 4+4=8. The values are between 1 and 7, inclusive.
Thus, the values in the intersection between the two inequalities are from 4-7 for 7-4+1=4 values that satisfy AC, namely 4, 5, 6, and 7 units.
+4622 Notice that AC splits the quadrilateral into two pieces.
ABC is a triangle as well as ADC.
By the Triangle Inequality for triangle ABC, AC must be greater than 6-3=3 and less than 6+3=9. The values are between 4 and 8, inclusive.
By the Triangle Inequaliyt for triangle ADC, AC must be greater than 4-4=0 and less than 4+4=8. The values are between 1 and 7, inclusive.
Thus, the values in the intersection between the two inequalities are from 4-7 for 7-4+1=4 values that satisfy AC, namely 4, 5, 6, and 7 units.
