## The big triangle brainteaser

By David Shaw, 17 April 2019

At Three Peaks School, they’re planning to build a gigantic triangle.

The sides have just arrived, on the back of some truly ridiculous trucks, and with police escort.

The longest side is 42 metres long, with the other two sides measuring 25 and 16 metres respectively.

Can you work out the area of the triangle assembled from these pieces?

Scroll down for the answer!

## Brainteaser answer

The lengths of any two sides of a triangle must add up to more than the length of the third side. If you put the two shorter sides end to end, you get a length of 41 metres, shorter than the long side. So there’s no way to make a triangle at all – the short sides are just too short!

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17 April, 2019 at 12:51 pm

Cop out!

If you have a side 42 metres long you can cut that to make any size triangle you want

The school would sack you as their triangle builder!

If you use 16 as the base you could have a 25x25x16 triangle which would look nice!

19 April, 2019 at 1:46 pm

I think i found the answer. You draw the triangle onto a sphere.

19 April, 2019 at 2:31 pm

“So there’s no way to make a triangle at all” Not so with non-Euclidean geometry.

19 April, 2019 at 10:50 pm

I got 200m^2 because 1/2xbxh = the area of a triangle.

= 1/2 x 16 x 25

= 200

But honestly I find this wouldn’t be a brain teaser without a twist. I love it.

6 September, 2020 at 11:15 am

You can make a triangle, with one side of 25 m and one side of 16 m, and the other ends of these two sides both touching the longest side.

However, you can’t use all of the longest side; if the angle between the 16 m and 25 m sides is a right angle (90°), then about 12.3 metres of the 42m side is sticking out from the triangle you’ve made, which has an area of 200 sq m.