WEBVTT
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Find the perimeter of triangle ๐ด๐ต๐ถ.
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Weโre asked to find the perimeter here.
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Thatโs the distance all the way round the outside of a shape.
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The triangle here is this smaller triangle, ๐ด๐ต๐ถ.
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In order to find the perimeter of triangle ๐ด๐ต๐ถ, we need to know the length of all three of the sides of this triangle.
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If we look at the line markings, we can see that the length ๐ท๐ถ, which is given as 14.1 centimeters, will be the same as the line ๐ถ๐ต and the line ๐ด๐ถ.
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So, these are also both 14.1 centimeters.
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Thereโs no immediate way to find the length of this line ๐ด๐ต, so letโs have a look at the angles that weโre given.
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Letโs consider this triangle ๐ด๐ถ๐ท.
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Now, weโre told that two lengths are the same, which means that this triangle ๐ด๐ถ๐ท is an isosceles triangle.
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It also means that weโll have two equal angles.
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We can then say that this angle ๐ท๐ด๐ถ must also be 30 degrees.
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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 ๐ด๐ถ๐ท.
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We would calculate 180 degrees subtract 30 degrees subtract 30 degrees.
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And as thatโs the same as subtracting 60 degrees, weโd be left with 120 degrees.
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Now, weโre still really interested in triangle ๐ด๐ต๐ถ.
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So, letโs see what we can find out about this triangle.
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If we use the fact that we have this straight line ๐ท๐ต and the fact that angles on a straight line add up to 180 degrees, we can find this angle ๐ด๐ถ๐ต.
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This angle will be equal to 180 degrees subtract 120 degrees, which is 60 degrees.
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We may feel at this point that weโre still no closer to finding the length of ๐ด๐ต, but letโs consider the type of triangle that ๐ด๐ต๐ถ is.
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Just like our previous triangle ๐ด๐ถ๐ท, we could say that ๐ด๐ต๐ถ is also an isosceles triangle, so it will also have two equal angles.
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Angle ๐ถ๐ด๐ต will be the same size as angle ๐ด๐ต๐ถ.
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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.
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So, now, what can we say about this triangle, ๐ด๐ต๐ถ?
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Itโs not just isosceles; it is, in fact, an equilateral triangle.
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We know this because in an equilateral triangle, all the internal angles are 60 degrees.
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And importantly for us, we know that all the sides in an equilateral triangle are the same length.
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This means that we now know the length of ๐ด๐ต.
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Itโs also 14.1 centimeters.
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We can now find the perimeter of triangle ๐ด๐ต๐ถ by adding 14.1, 14.1, and 14.1 or alternatively three multiplied by 14.1.
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This will give us our final answer of 42.3 centimeters.