Video Transcript
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. Find the value of π plus π minus
π, giving the answer to the nearest centimeter.
The first part of this question is
to calculate the lengths π, π, and π. 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, π, and π 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 is 18
centimeters. Seven multiplied by six is equal to
42. Therefore, π has length 42
centimeters. Finally, nine multiplied by six is
equal to 54. So the length of side π 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 plus π minus π. 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 plus π minus π 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 donβt need to
round in this question.
