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π΄π΅πΆ is a triangle, where the perimeter is 114 centimeters and the ratio between the lengths π, π, and π is three to seven to nine.
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Find the value of π plus π minus π, giving the answer to the nearest centimeter.
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The first part of this question is to calculate the lengths π, π, and π.
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We know the perimeter of the triangle is 114 centimeters and the ratio of the lengths is three to seven to nine.
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We begin by adding the ratios.
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Three plus seven plus nine is equal to 19.
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As we have 19 parts in total, we need to divide 114 centimeters by 19.
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114 divided by 19 is equal to six.
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This means that one part of the ratio is equal to six centimeters.
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We recall that the ratio of the lengths π, π, and π was three to seven to nine.
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This means we need to multiply all of these by six centimeters.
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Three multiplied by six is equal to 18.
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Therefore, the length π is 18 centimeters.
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Seven multiplied by six is equal to 42.
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Therefore, π has length 42 centimeters.
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Finally, nine multiplied by six is equal to 54.
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So the length of side π is 54 centimeters.
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It is worth checking at this stage that our three values sum to 114 centimeters.
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We now need to calculate the value of π plus π minus π.
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We need to add 18 to 42 and then subtract 54.
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18 plus 42 is equal to 60.
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Subtracting 54 from this gives us an answer of six.
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The value of π plus π minus π is therefore equal to six centimeters.
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We were asked to give our answer to the nearest centimeter.
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However, our answer is already an integer value.
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This means that we donβt need to round in this question.