Perimeter Of The Isosceles Triangle

About Perimeter Of The Isosceles Triangle

The perimeter of the isosceles triangle is the sum of its sides or the total length of its boundary. If a triangle has two equal sides and two equal angles, it is called an isosceles triangle. Let's look at some solved cases to learn more about the perimeter of an isosceles triangle.

Perimeter of Isosceles Triangle
An isosceles triangle's perimeter is equal to the sum of its three sides. The perimeter of an isosceles triangle is twice the equal side plus the difference side because it has two equal sides. Inches (in), yards (yd), millimetres (mm), centimetres (cm), and metres are examples of linear units (m). In the next section, we'll look at the formula for calculating the perimeter.

Perimeter of Isosceles Triangle Formula
An isosceles triangle's perimeter is calculated by summing the lengths of all three sides. Because an isosceles triangle has 2 equal sides, the perimeter may be determined using the base and one of the equal sides. The perimeter of isosceles triangle is calculated using the following formula:
- Perimeter of the isosceles triangle (P) = 2a + b
- where, a = the length of the equal sides; b = the length of the base (unequal side)
- Derivation of the formula: Examine the diagram below, which will assist us in calculating the perimeter of an isosceles triangle. Consider the isosceles triangle ABC, with side AB equal AC. If the equal sides are labelled 'a,' and the unequal sides are labelled 'b,' the sum of all the sides is AB + AC + BC, or a + a + b. So the perimeter of an isosceles triangle is : 2a + b
Perimeter of Isosceles Triangle ABC = 2a + b
- Add the lengths of all three sides of an isosceles right-angled triangle to find its perimeter. Because it's a right-angled triangle, one of the sides is the hypotenuse, while the other two are equal. If the hypotenuse is 'h' units long and the other two sides are 'l' units long, then the perimeter of an isosceles right triangle is: Isosceles right triangle perimeter = h + l + l To understand the dimensions and formula of an isosceles right triangle, look at the diagram below.
- Perimeter of an Isosceles Right Triangle PQR = h + 2l
  - The perimeter of an isosceles right triangle is :- P = h + 2l.
  - The perimeter of an isosceles right triangle in 2 different cases is given below.
    - If we apply the Pythagoras theorem to the figure, we get h = √(l²+ l²) = √2 × l. This means h = √2 × l, which can be written as: l = h/√2. Values can be substituted with one another if one of them is unknown.
    - When the length of the equal side is given: If the length (l) is given, then the perimeter of an isosceles right triangle (P) = 2l + (√2)l = (2 + √2)l
    - When the hypotenuse is given: If the hypotenuse (h) is given, then perimeter of an isosceles right triangle (P) = h + 2(h/√2) = h(1 + √2)
  - Two congruent angles in isosceles right triangle measure 45° each.
- Important Notes on Perimeter of Isosceles Triangle
  - In a triangle if it has 2 equal sides then it is an isosceles triangle.
  - Since an isosceles triangle has 2 equal sides, its perimeter can be calculated if the base and the equal sides are known.
  - The formula to calculate the perimeter of the isosceles triangle is P = 2a + b where 'a is the length of two equal sides & 'b' is the base of the triangle.
  - The perimeter of an isosceles right triangle can be calculated with help of the formula: P = h + 2l, where 'h' is the length of hypotenuse & 'l' is the length of the adjacent sides.