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The green and red lines show the maximum possible heights when we use AC and AB respectively as the base.

So the area increases as we move B to U (left) and then move C to V.

However, as we move C to V, point U also moves. So we can increase the area further by moving B to the new position of U - and then moving C to the new position of V.

What happens to the shape of the triangle as we continue to move B and C in this way? Us this worksheet to find out.