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Triangle ABC and ABD share side AB. Triangle ABC has area Q and Triangle ABD has area R. If AD is longer than AC and BD is longer than BC, which of the following could be true?

I) R > Q

II) R= Q

III) R < Q

Triangle ABC and ABD share side AB. Triangle ABC has area Q and Triangle ABD has area R. If AD is longer than AC and BD is longer than BC, which of the following could be true?

I) R > Q

II) R= Q

III) R < Q

I have tried every drawing of the sides and stuff but it hasn't worked out yet.

All three can be true. In the diagrams, the red lines are parallel to AB which is drawn as the base for both triangles. The red lines are also equidistant from AB. Since area = (1/2) base * height and the bases are the same for each triangle, we only need to compare the heights. The height is the perpendicular distance of the third point of each triangle to the line passing through AB.

R > Q

since D is past the red line, R > Q

R = Q

since D is on the red line, R = Q

R < Q

since D is behind the red line, R < Q

in all three diagrams AD > AC and BD > BC