Introduction

A triangle is a closed 2D polygon with three straight sides and when two of the sides of such a figure are equal these are called isosceles triangles. In an isosceles triangle, the opposite angles of the equal sides are also equal. An isosceles triangle can also be a right-angle isosceles triangle. The perimeter of isosceles triangle is the sum total of the length of its sides or the total length of the boundaries enclosing the triangular region.

Cuemath explains the topic in a very efficient and easy to understand manner.

In this article, the perimeter of the isosceles triangle is explained by giving bullet points and quick to understand examples.

Some properties of an isosceles triangle

  1. Two sides of an isosceles triangle are equal and congruent.
  2. Angles opposite to the equal sides of an isosceles triangle are equal.
  3. The equal angles form of base angles of the triangle.
  4. The angle that is different from the other two angles is called the apex angle.
  5. The Converse angle theorem of the isosceles triangle says that if two angles of any triangle are equal, we can conclude the sides opposite to them are also equal.

The perimeter of Isosceles Triangles

Two Greek words ‘peri’ meaning around and ‘metron’ meaning measure come together to form a single term perimeter which means the measure of boundaries. 

The perimeter of an isosceles triangle can be measured by adding up all the sides of the triangle, i.e. 

The perimeter of the isosceles triangle= sum of all sides

Right Isosceles Triangle

The right isosceles triangle is one in which one angle is equal to 90 degrees and the base and the height are always equal. The side opposite to the right angle that is 90° forms the hypotenuse.

So, the perimeter of a right-angled isosceles triangle can be found out by adding twice the equal side with the length of the hypotenuse.

Perimeter of isosceles triangle = 2*s + b, where s represents the length of two congruent sides and b is the length of the base.

The perimeter of the right isosceles triangle = 2*base + hypotenuse.

*Note: The perimeter of the isosceles triangle changes with the change in the value of congruent sides and base.

The Practical Uses of Perimeter of the Isosceles Triangle are:

  1. Fencing off a triangular area to plot a crop in a field.
  2. Isosceles triangles appear in the architecture as the shapes of pediments and gables.
  3. The architecture of the Middle Ages shows the importance of isosceles triangle shape.
  4. In graphic design and decorative arts, isosceles triangles have been a frequent design element in cultures around the world.
  5. The perimeter of an isosceles triangle can be used to cut a triangular plot of land.
  6. The perimeter of the isosceles triangle may help to calculate the distance traveled along with a figure or an area of land.

Now, at last, let us learn how to find the perimeter of an isosceles triangle with an example: 

Example1:

Find the perimeter of the isosceles triangle when the length of the two equal sides is 5 cm and the third side is 6 cm.

Solution: 

Each equal side= 5cm.

Third side= 6cm.

We know that the formula to calculate the perimeter of an isosceles triangle is P = 2s + b units. Therefore, the perimeter of an isosceles triangle = 2*5+6= 16 cm.

Example 2: 

Calculate the distance traveled by a man while walking along the fence of a triangular field whose two sides are equal to 3 m and the longest side is3√2m. (The two equal sides make an angle of 90 degrees between them).

Solution:

As it is given that the angled weight between the two equal sides is 90 degrees so we will conclude that it is an isosceles right-angled triangle.

Hence two equal sides that make the angle of 90 degrees between them make up the base and the height =3m each.

The hypotenuse = 3√2m

Using the formula of the perimeter of an isosceles triangle

Perimeter (the distance covered by man) = 2*3+3√2 m

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