## Starter of the Day

If the base of this triangle became 8cm but the other sides remained 5cm, how much would its area increase?

• Transum,
•
• At the time of writing this is a new starter and not many people have had a chance to score it. Though it is going to be perhaps out of reach of the younger pupils, those with a knowledge of Pythagoras' Theorem should find it quite easy. The height of the triangle works out to be a whole number in both the before and after situations and from that, the surprising result can be found. A complete explanation can be found in the answers below. Please feedback any thoughts on this.
• Dave, Australia
•
• It is unclear whether the other lengths of the triangle adjust along with the base or if they remain constant. If they (the 5cm sides) remain constant the area will be unchanged - however if they do not the area will be increasing...
• Joe Young, Chirstchurch
•
• This doesn't help, it doesn't really tell us what to do. Also it gives no place to answer and find out if we have even got it right. My students are unsure what to do.

[Transum: Thanks for your feedback Joe. This activity is designed as a lesson Starter to be projected in front of a class at the beginning of a lesson. The teacher can then lead a discussion with pupils about what the solution might be. The answer appears lower down this page for teachers who are signed in.]
• Elliot Oliver, Temuka
•
• Rephrasing what Dave and Joe said, this starter isn't the best. It is not very clear about if the hypotenuses of the two triangles stay the same, as well as if the height changes. To clarify that would be great.
• Yolax, Australia
•
• I must disagree with the critical comments this is a beaut starter it clearly states that the 5cm sides remain the same. The area will not change, so that is the learning moment revel in it!
• Monday, August 5, 2024
• The previous comments have me confused, leading me to believe that those teachers must have completed an earlier iteration of this task.
To their points: 1) the question clearly states that the top sides remain the same, and 2) the hypotenuse doesn't even factor in to this one as it is not a right-angled triangle.
As my class is doing area at the moment, I'll be using this one in my class this week!

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.

Previous Day | This starter is for 5 August | Next Day

## Extension

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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## Maths T-Shirts

Here is the URL which will take them to a related student activity.

Transum.org/go/?to=pythag
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