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What is the formula for the perimeter of a triangle?

The perimeter of a triangle is calculated by summing the lengths of its three sides.

To determine the perimeter of a triangle, you simply add the lengths of all three sides together. If the sides are denoted as aa, bb, and cc, the formula for the perimeter PP is given by:

P=a+b+cP = a + b + c

This formula is applicable to all types of triangles, including scalene, isosceles, and equilateral triangles.

For instance, consider a triangle with side lengths of 5cm5 \, \text{cm}, 7cm7 \, \text{cm}, and 10cm10 \, \text{cm}. To find the perimeter, you would calculate:

5+7+10=22cm5 + 7 + 10 = 22 \, \text{cm}

In the case of an equilateral triangle, where all three sides are of equal length, the formula simplifies to:

P=3aP = 3a

Here, aa represents the length of one side. For example, if each side of an equilateral triangle measures 6cm6 \, \text{cm}, the perimeter would be calculated as follows:

P=3×6=18cmP = 3 \times 6 = 18 \, \text{cm}

Understanding how to calculate the perimeter is essential, as it allows you to determine the total distance around the triangle. This knowledge can be particularly useful in various practical applications, such as planning the fencing for a triangular garden or framing a triangular piece of artwork. Always ensure that the units of measurement for all sides are consistent before performing the addition to obtain an accurate perimeter.

Answered by: Prof. Peter Brown
IB Maths Tutor
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