



 
Hi Panny, Many triangles have the same perimeter but different areas. Suppose I start with everyone's favourite right triangle, the one with sides of length 3, 4 and 5 units. This triangle is half the rectangle with sides of length 3 and 4 units so its area is half the area of the rectangle. Hence its area is $\frac12 3 \times 4 = 6$ square units. Its perimeter is $3 + 4 + 5 = 12$ units. Here is another triangle with a perimeter of 12 units. It is the isosceles triangle $ABC$ with base $AB$ of length 2 units and hence, since its perimeter is 12 units, the sides have length \[\frac12 (12  2) = 5 \mbox{ units. }\] P is the midpoint of $AB$ and hence the height$PC$ of triangle $ABC$ can be found using Pythagoras' Theorem \[PC = \sqrt{5^2  1^2} = \sqrt{24} = 4.8990 \mbox{ units.}\] Thus the area of triangle $ABC$ is \[\frac12 AB \times PC = 1 \times 4.8990 = 4.8990 \mbox{ square units.}\] So this triangle has a perimeter of 12 units and yet its area is less than 5 square units. That was fun! Let's do it again. This time make $AB = 0.2$ units. What are the lengths of the other two sides if the perimeter is to remain as 12 units? What is the area of the triangle? What if $AB = 0.002$ units or $0.0002$ units or $0.0000002$ units? Penny  


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