If the base of this triangle became 8cm but the other sides remained 5cm, how much would its area increase?
Topics: Starter  Area  Mensuration  Problem Solving  Pythagoras
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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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Teacher, do your students have access to computers such as tablets, iPads or Laptops? This page was really designed for projection on a whiteboard but if you really want the students to have access to it here is a concise URL for a version of this page without the comments: Transum.org/go/?Start=August5 However it would be better to assign one of the student interactive activities below. 

Here is the URL which will take them to a related student activity.
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 equalarea bases and the length of base giving the maximum area: