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
How did you use this starter? Can you suggest
how teachers could present or develop this resource? Do you have any comments? It is always useful to receive
feedback and helps make this free resource even more useful for Maths teachers anywhere in the world.
Click here to enter your comments.
If you don't have the time to provide feedback we'd really appreciate it if you could give this page a score! We are constantly improving and adding to these starters so it would be really helpful to know which ones are most useful. Simply click on a button below:
This starter has scored a mean of 2.8 out of 5 based on 159 votes.
Previous Day  This starter is for 5 August  Next Day
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?
Your access to the majority of the Transum resources continues to be free but you can help support the continued growth of the website by doing your Amazon shopping using the links on this page. Below is an Amazon search box and some items chosen and recommended by Transum Mathematics to get you started.
Apple iPad ProThe analytics show that more and more people are accessing Transum Mathematics via an iPad as it is so portable and responsive. The iPad has so many other uses in addition to solving Transum's puzzles and challenges and it would make an excellent gift for anyone. The redesigned Retina display is as stunning to look at as it is to touch. It all comes with iOS, the world's most advanced mobile operating system. iPad Pro. Everything you want modern computing to be. more... Before giving an iPad as a Christmas gift you could add a link to iPad Maths to the home screen. 
A Compendium Of Mathematical MethodsHow many different methods do you know to solve simultaneous equations? To multiply decimals? To find the nth term of a sequence? A Compendium of Mathematical Methods brings together over one hundred different approaches from classrooms all over the world, giving curious mathematicians the opportunity to explore fascinating methods that they've never before encountered. If you teach mathematics to any age group in any country, you are guaranteed to learn lots of new things from this delightful book. It will deepen your subject knowledge and enhance your teaching, whatever your existing level of expertise. It will inspire you to explore new approaches with your pupils and provide valuable guidance on explanations and misconceptions. more... 
Teacher, do your students have
access to computers? 

Here a concise URL for a version of this page without the comments.
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: