Quadrilateral has right angles at B and D, and AC = sqrt(65). If ABCD has distinct integer side lengths, then what is the area of ABCD?
+128408 We need to find two Pythagorean Triples here such that
a^2 + b^2 = 65
There are two pairs that work (8,1) and ( 7, 4)
So.....we can let AB = 8 ,BC = 1, CD = 7 and DA = 4
We have two right triangles sharing the same hypotenuse ( AC)
The area of the quadrilateral is (1/2) [ (8) (1) + (7) (4) ] = (1/2) [ 8 + 28 ] = (1/2) (36) = 18
