PLEASE!! I have one last question?

Figure ABCD is a kite. The length of side AD is (x + 4) inches, the length of side CD is (2x – 3) inches, and the length of side AB is 12 inches. The measure of Angle A is equal to the measure of angle C .

Question

PLEASE!!  I have one last question? 

Figure ABCD is a kite. The length of side AD is (x + 4) inches, the length of side CD is (2x – 3) inches, and the length of side AB is 12 inches. The measure of  Angle A is equal to the measure of angle C .

anonymous · Answer

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anonymous · Answer

Assume AD=AB. Since it's a kite, DC=BC. Draw line BD. By isosceles triangles, we have <CDB=<CBD and <ADB=<ABD. By ASA, triangle ADB~=CDB so CD=AD and solving gives CD=11. However, we know AD=AB=12. Contradiction. Thus the only other case is that AD=AC=11 and BC=12.

anonymous · Answer

Thanks for the explanation, slightly confusing. :P so the length is 11?

anonymous · Answer

yes lol. just show that AD=DC and AD=/=AB by showing the contradiction the latter  case implies.