Quadrilateral ABCD has right angles at B and D, and AC = 3. If ABCD has two sides with distinct integer lengths, then what is the area of ABCD? Express your answer in simplest radical form.
+1094 Hint: If you draw the picture out, you will see that AC is a diagonal. (because no two right angles can be together without forming a rectangle)
Further Hint: This means that you have created two right triangles. What theorem do they follow? (Pythagorean?)
Even further hint: What are the only two integers that can create a hypotenuse of 3? (The two integers that are less then 3.....right?)
Even even further hint: Can you use a theorem to find the other sides?
In general, you should draw a shape of it has anything to do with geometry. Many geometry questions include shapes, but if there is not one, try drawing it yourself. You will see that it helps a LOT.
:)
