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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
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AC divides the quadrilateral into two triangles, triangle(ABC) and triangle(ADC)

 

Each two sides of the triangle must have a sum greater than the third side.

 

In triangle(ABC), AC can be 4, 5, 6, 7, or 8

 

In triangle(ADC), AC can be 1, 2, 3, 4, 5, 6, or 7.

 

Combining the two, we get 4, 5, 6, or 7.

 Apr 10, 2020

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