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Isosceles Triangle Perimeter (P = 2a + b)

Two equal sides make perimeter a short addition problem once you label the base.

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Triangle sketch and measuring tools on archival paper

Quick Answer

P = 2a + b when a is the equal side and b is the base.

Formula

  • P = a + a + b
  • Equal sides opposite equal angles

Introduction

The calculator accepts three side fields: enter the equal length twice and the base once.

Isosceles triangles show up in roofs, symmetric plots, bridge trusses, and many standardized test diagrams where two edges match.

Start from the general rule in what is the perimeter of a triangle if you want the definition before you use shortcuts.

Main Content

Equal-side properties

Only two sides match. The third side is the base, and it often sits opposite the angle between the equal sides on diagrams.

Geometric interpretation: symmetry across an altitude from the vertex between the equal sides divides the triangle into mirror halves.

Measurement examples include a triangular plot with two 20 m frontages and a 15 m rear edge, giving P = 55 m.

Common homework problems state two equal sides in words without drawing tick marks, so underline matching lengths before you add.

Formula

  • P = 2a + b

Example: equal sides 7, base 4 → P = 7 + 7 + 4 = 18.

You may also write P = 2(7) + 4. Both forms are equivalent when labeling is consistent.

If a problem gives perimeter and the base, solve for the equal side with algebra before you move on.

When all three sides differ with no pairs, the triangle is scalene and you should follow the scalene triangle perimeter method instead of forcing P = 2a + b.

Method

Label first, then substitute, then add.

  1. Mark equal sides Use tick marks from the diagram or the problem statement.
  2. Identify base The side that appears once in the sum is b.
  3. Compute 2a + b Or add a + a + b if you prefer to see every side.
  4. Check with the calculator Enter the three side lengths to confirm mental arithmetic.

Example

Equal sides 5 in, base 8 in → P = 5 + 5 + 8 = 18 in.

Equal sides 12 ft, base 9 ft → P = 33 ft of fence along a symmetric triangular section.

A roof panel described as isosceles with legs 6 m and base 4 m needs P = 16 m along the outer edges you are quoting.

FAQ

What if I only know the equal sides?
You still need the base length or another fact to find perimeter.
Can an isosceles triangle be right?
Yes. The 45-45-90 triangle is isosceles. Perimeter still sums all three sides.

Conclusion

Label equal sides before you substitute into P = 2a + b.

See more mixed cases in perimeter examples and check results at /#calculator.

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