A triangle problem to solve
I have another neat problem for you to solve. This one should be accessible to middle schoolers on up. The sides of triangles A and B measure 5, 5, 8 and 5, 5, 6 respectively. What is the ratio of the area of triangle A to that of triangle B? Express in simplest a:b form. This problem is original to John Morse. He is a local mathematics researcher/ author/tutor/computer programmer in Delmar, NY, and has written this problem to help learners use creative and problem-solving skills in various ways. And I think this problem can indeed help in that - it can be solved in many different ways. [update - solution follows] I like this problem because there are many ways to solve it and to use it with different grade-level students - such as is already mentioned in the comments. 1) You could use this as a drawing and measuring exercise with 6th or 7th graders who have learned to do compass and ruler constructions. Once they know how to construct a triangle given its three sides (or see here ...