Question Video: Finding the Perimeter of a Triangle Mathematics

Find the perimeter of โ–ณ๐ด๐ต๐ถ.


Video Transcript

Find the perimeter of triangle ๐ด๐ต๐ถ.

Weโ€™re asked to find the perimeter here. Thatโ€™s the distance all the way round the outside of a shape. The triangle here is this smaller triangle, ๐ด๐ต๐ถ. In order to find the perimeter of triangle ๐ด๐ต๐ถ, we need to know the length of all three of the sides of this triangle. If we look at the line markings, we can see that the length ๐ท๐ถ, which is given as 14.1 centimeters, will be the same as the line ๐ถ๐ต and the line ๐ด๐ถ. So, these are also both 14.1 centimeters. Thereโ€™s no immediate way to find the length of this line ๐ด๐ต, so letโ€™s have a look at the angles that weโ€™re given.

Letโ€™s consider this triangle ๐ด๐ถ๐ท. Now, weโ€™re told that two lengths are the same, which means that this triangle ๐ด๐ถ๐ท is an isosceles triangle. It also means that weโ€™ll have two equal angles. We can then say that this angle ๐ท๐ด๐ถ must also be 30 degrees. We should remember that the angles in a triangle add up to 180 degrees, which means that we can find the size of this angle ๐ด๐ถ๐ท. We would calculate 180 degrees subtract 30 degrees subtract 30 degrees. And as thatโ€™s the same as subtracting 60 degrees, weโ€™d be left with 120 degrees.

Now, weโ€™re still really interested in triangle ๐ด๐ต๐ถ. So, letโ€™s see what we can find out about this triangle. If we use the fact that we have this straight line ๐ท๐ต and the fact that angles on a straight line add up to 180 degrees, we can find this angle ๐ด๐ถ๐ต. This angle will be equal to 180 degrees subtract 120 degrees, which is 60 degrees. We may feel at this point that weโ€™re still no closer to finding the length of ๐ด๐ต, but letโ€™s consider the type of triangle that ๐ด๐ต๐ถ is.

Just like our previous triangle ๐ด๐ถ๐ท, we could say that ๐ด๐ต๐ถ is also an isosceles triangle, so it will also have two equal angles. Angle ๐ถ๐ด๐ต will be the same size as angle ๐ด๐ต๐ถ. Using the fact that the angles in a triangle add up to 180 degrees, these two angles must therefore add together to give 120 degrees, meaning that both of these angles will be 60 degrees. So, now, what can we say about this triangle, ๐ด๐ต๐ถ? Itโ€™s not just isosceles; it is, in fact, an equilateral triangle.

We know this because in an equilateral triangle, all the internal angles are 60 degrees. And importantly for us, we know that all the sides in an equilateral triangle are the same length. This means that we now know the length of ๐ด๐ต. Itโ€™s also 14.1 centimeters.

We can now find the perimeter of triangle ๐ด๐ต๐ถ by adding 14.1, 14.1, and 14.1 or alternatively three multiplied by 14.1. This will give us our final answer of 42.3 centimeters.

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