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# help! i've been stuck on this for over an hour T-T

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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.

Apr 10, 2020

#4
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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.

Apr 10, 2020

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dont repost when its only been 3 minutes

Apr 10, 2020
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sorry, i'm kinda new to this whole thing and I realized that I did that on accident :(

infiresman  Apr 10, 2020
#3
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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.

Apr 10, 2020
#5
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Posted twice by accident...

tertre  Apr 10, 2020
#4
+1

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.

tertre Apr 10, 2020