By how much would the area of this triangle increase if its base was enlarged to 8cm?
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Can you find another pair of triangles that, like those above, surprisingly have the same areas?
What is the length of the base which gives the triangle mentioned above the maximum area?
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A first thought might be that the graph of area against length of base is symetrical but it is not. A graphic calculator will help you identify equal-area bases and the length of base giving the maximum area: