Since an isosceles triangle has two equal sides, the perimeter is twice the equal side plus the different side.Ģ: How to find the Perimeter of an Isosceles Triangle?Īnswer: The perimeter of an isosceles triangle is the total length of its boundary. The third side of the triangle measures 6 units.įrequently Asked Questions on Isosceles Triangle Perimeterġ: What is the Perimeter of Isosceles Triangle?Īnswer: The perimeter of an isosceles triangle is the sum of all the three sides. Substituting the given values in the above formula, Using the formula for the perimeter of isosceles triangle = 2a + b Given, Perimeter = 12 units, a = 3 units, b = ? Solution: Let the third side of the isosceles triangle be ‘b’ ![]() Find out the length of the third side of the triangle if the equal sides measure 3 units each. The perimeter of the given isosceles triangle is 26 cm.Įxample 2: The perimeter of an isosceles triangle is 12 units. In this case, the length of one equal side (a) = 10 cm base (b) = 6 cm To find the perimeter of isosceles triangle, we use the formula: perimeter = 2a + b. Solved Examples on Isosceles Triangle PerimeterĮxample 1: What is the perimeter of an isosceles triangle when the length of one of the equal sides = 10 cm and the base = 6 cm? The perimeter of an isosceles right triangle can be calculated with the help of the formula: P = h + 2l, where ‘h’ is the length of the hypotenuse and ‘l’ is the length of the adjacent sides. The formula to calculate the perimeter of an isosceles triangle is P = 2a + b where ‘a’ is the length of the two equal sides and ‘b’ is the base of the triangle. ![]() Since an isosceles triangle has two equal sides, its perimeter can be calculated if the base and the equal sides are known. ![]() Here is a list of a few points that should be remembered while studying the perimeter of an isosceles triangle:Ī triangle is considered to be an isosceles triangle if it has two equal sides. Important Notes on Perimeter of Isosceles Triangle It should be noted that the two congruent angles in the isosceles right triangle measure 45° each. When the hypotenuse is given: Referring to the explanation given above, if the hypotenuse (h) is given, then the perimeter of an isosceles right triangle will be (P) = h + 2(h/√2) = h + √2h = h(1 + √2) When the length of the equal side is given: Referring to the explanation given above, if the length (l) is given, then the perimeter of an isosceles right triangle will be (P) = 2l + (√2)l = (2 + √2)l These values can be substituted with each other if one of them is not known. This means h = √2 × l, which can also be written as: l = h/√2. If we apply the Pythagoras theorem in the figure, we get h = √(l2+ l2) = √2 × l. Now, let us find the perimeter of an isosceles right triangle in 2 different scenarios given below. Observe the following figure to understand the dimensions and the formula of an isosceles right triangle.Īs given in the figure, the perimeter of an isosceles right triangle is P = h + 2l. If the length of the hypotenuse is ‘h’ units and the lengths of the other two sides are ‘l’, then the perimeter of an isosceles right triangle would be: Perimeter of isosceles right triangle = h + l + l. Since it is a right-angled triangle, one of its sides is the hypotenuse and the other two sides are equal. The perimeter of an isosceles right-angled triangle can be found by adding the length of all its three sides. Therefore, the perimeter of an isosceles triangle is : 2a + b. Now, if the equal sides are named as ‘a’ and the unequal side is named as ‘b’, the sum of all its sides will be: AB + AC + BC, or, a + a + b. Let us consider an isosceles triangle ABC in which side AB = AC. The formula used to find the perimeter of an isosceles triangle is: Perimeter of isosceles triangle (P) = 2a + b where, a = the length of the equal sides b = the length of the base (unequal side).ĭerivation of the formula: Observe the figure given below which will help us to derive the formula for the perimeter of an isosceles triangle. Since an isosceles triangle has two equal sides, its perimeter can be calculated if the base and one equal side is known. The perimeter of an isosceles triangle is calculated by adding the length of all its three sides. Let us understand the formula to find the perimeter in the next section. It is measured in linear units such as inches (in), yards (yd), millimeters (mm), centimeters (cm), and meters (m). Since an isosceles triangle has 2 equal sides, the perimeter is twice the equal side plus the different side. The perimeter of an isosceles triangle is the sum of all the three sides.
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