# Perimeter of Isosceles Triangle

By the end of this lesson, you will be able to

- describe perimeter of isosceles triangle.
- interpret the relation among the base and equal sides of an isosceles triangle.
- derive the formula for perimeter of isosceles triangle.
- represents examples of isosceles triangle.
- calculate the perimeter of an isosceles triangle with example worksheet.

## Perimeter of Isosceles Triangle

The sum of the base and twice the equal sides is called the perimeter of isosceles triangle. The two sides of an isosceles triangle are equal. Consequently, the two angles opposite of two equal sides are also equal to each other. Thus the perimeter of isosceles triangle can also be defined as the sum of the base and twice the side opposite of equal angle.

An isosceles triangle

Thus, there are two equal sides of an isosceles triangle. Equivalently, the two angles opposite its two equal sides are always equal measuring.

The two equal sides are known as legs while the third side called the base. This is a special type of triangle in terms of side.

## Isosceles Triangle Perimeter Formula

Suppose, the length of the base of an isosceles triangle is b and equal side is a. Then isosceles triangle perimeter formula is (2a+b).

If the base and equal side of an isosceles triangle are b unit and a unit respectively; and the perimeter is P,

P = (2a + b) unit

## Apps for finding the perimeter of isosceles triangle

equal side a:

base b:

Perimeter: 14.00

## Relation Between Base and Equal Sides

There is an important relation among the base and sides of an isosceles triangle. The length of the equal side must be greater than half the length of the base of the isosceles triangle. This relation comes from the sum of any two sides of a triangle is greater than the third one.

For a, b and c are the length of any scalene triangle,

a + c > b.

If a and c are the equal sides and b is the base of isosceles triangle, the relation above takes form:

a + a > b

or, 2a > b

or, a > 12 b

∴ equal side > 12 × base

If a and b are the equal side and base of isosceles triangle respectively,

a > 12 b

∴ equal side > 12 × base

## Perimeter of Isosceles Triangle Worksheet

The base and the equal side of an isosceles triangle are 5 cm and 7 cm.

(a) Draw the isosceles triangle.

(b) Find the perimeter.

(c) If the length of the base and the equal side of an another isosceles triangle are equal to the equal side and the base of the first isosceles triangle respectively, find the perimeter of the second isosceles triangle.

Solution(a): The figure of the required isosceles triangle is as follows:

An isosceles triangle showing in the figure that shows its base and equal sides. Here the base is 5 cm and equal sides are 7 cm and 7 cm.

Solution(b): Let the length of the base be b = 5 cm and equal side be a = 5 cm.

If the perimeter is P,

P = (2a + b) unit

or, P = (2 ×7 + 5) cm

or, P = (14+5) cm

∴ P = 19 cm

Solution(c): Length of the base of the first triangle is 5 cm.

And length of the equal side of the first triangle is 7 cm.

According to Question,

Base of second triangle = equal side of first triangle.

And equal side of second triangle = base of first triangle.

Hence, the length of the base of second triangle, b = 7 cm and equal side is a = 7 cm.

If the perimeter of the second triangle is P_{2nd},

P_{2nd} = (2a+b) unit

or, P_{2nd} = (2 × 5 + 7) cm

or, P_{2nd} = (10+7) cm

∴ P_{2nd} = 17 cm