Question Video: Properties of Proportion Involving Triangles Mathematics

𝐴𝐡𝐢 is a triangle, where the perimeter is 114 cm and the ratio between the lengths π‘Ž, 𝑏, and 𝑐 is 3 : 7 : 9. Find the value of π‘Ž + 𝑏 βˆ’ 𝑐, giving the answer to the nearest centimeter.

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Video Transcript

𝐴𝐡𝐢 is a triangle, where the perimeter is 114 centimeters and the ratio between the lengths π‘Ž, 𝑏, and 𝑐 is three to seven to nine. Find the value of π‘Ž plus 𝑏 minus 𝑐, giving the answer to the nearest centimeter.

The first part of this question is to calculate the lengths π‘Ž, 𝑏, and 𝑐. We know the perimeter of the triangle is 114 centimeters and the ratio of the lengths is three to seven to nine. We begin by adding the ratios. Three plus seven plus nine is equal to 19. As we have 19 parts in total, we need to divide 114 centimeters by 19. 114 divided by 19 is equal to six. This means that one part of the ratio is equal to six centimeters.

We recall that the ratio of the lengths π‘Ž, 𝑏, and 𝑐 was three to seven to nine. This means we need to multiply all of these by six centimeters. Three multiplied by six is equal to 18. Therefore, the length π‘Ž is 18 centimeters. Seven multiplied by six is equal to 42. Therefore, 𝑏 has length 42 centimeters. Finally, nine multiplied by six is equal to 54. So the length of side 𝑐 is 54 centimeters. It is worth checking at this stage that our three values sum to 114 centimeters.

We now need to calculate the value of π‘Ž plus 𝑏 minus 𝑐. We need to add 18 to 42 and then subtract 54. 18 plus 42 is equal to 60. Subtracting 54 from this gives us an answer of six. The value of π‘Ž plus 𝑏 minus 𝑐 is therefore equal to six centimeters. We were asked to give our answer to the nearest centimeter. However, our answer is already an integer value. This means that we don’t need to round in this question.

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