How this instrument works
Three lengths make up a triangle's entire boundary, and their sum defines its perimeter: P = a + b + c. Knowing any two of those pieces alongside the total leaves only one unknown, recovered by plain subtraction — sideC = perimeter − sideA − sideB. No angle, no square root, and no assumption about the shape's proportions enters into that single step.
That last point is worth dwelling on, because it is the whole reason this page exists separately from the right-triangle side solvers already on this site. Those pages recover a missing length from the Pythagorean relation, a² + b² = c², which only holds when one corner sits at exactly ninety degrees. This page makes no such assumption — it works from the perimeter definition alone, so it applies equally to a right triangle, an obtuse one, or any other figure, as long as the total and two of the three lengths are already known.
The trade-off is that this method needs a genuinely different starting fact than a Pythagorean solver does. Knowing two legs of a right triangle is enough to find the hypotenuse without ever touching the perimeter; knowing the perimeter and two lengths here needs no right angle at all, but it does need that total figure measured or given up front, something a Pythagorean approach never asks for.
- Enter the triangle's total boundary length into Perimeter.
- Enter one known side length into Side a and the other into Side b.
- Read Side c (missing): the perimeter minus both known lengths, in one subtraction.
- Confirm the three lengths satisfy the triangle inequality, since not every trio of numbers closes into an actual shape.
Worked example — perimeter 12, sides 3 and 4
A triangle has a known perimeter of 12, with two of its three sides measuring 3 and 4. The missing third length falls out directly: c = 12 − 3 − 4 = 5 — the familiar 3-4-5 triangle, recovered here from its perimeter and two sides rather than assembled from a right angle.
A perimeter of 15 with two known sides of 5 and 5 gives c = 15 − 5 − 5 = 5, an equilateral triangle recovered the same way. A third case, perimeter 20 with sides 7 and 8, gives c = 20 − 7 − 8 = 5 too — three entirely different triangles, all landing on the identical missing length of 5 purely by how their particular numbers happen to subtract out.
Questions
How do I find a missing triangle side from the perimeter?
Subtract the two known lengths from the total: c = perimeter − a − b. A perimeter of 12 with sides 3 and 4 gives c = 12 − 3 − 4 = 5, with no angle or square root involved at any point in that subtraction.
Does this only work for right triangles?
No — it works for any triangle at all, since it comes from the plain perimeter definition, P = a+b+c, rearranged, rather than from the Pythagorean theorem. A right angle is never assumed or required for this particular subtraction to hold.
How is this different from the right-triangle side solvers on this site?
Those pages recover a missing length from a² + b² = c², which only holds when one corner is exactly ninety degrees. This page instead uses the perimeter definition alone, so it applies to any triangle shape, provided the total perimeter and two of the three lengths are already known.
What if the two known sides already add up to the full perimeter or more?
Then no valid triangle exists, since the missing length would come out to zero or negative, and a length can't be zero or less in a real shape. The two known sides together must stay below the total perimeter for a genuine third length to remain.
Does it matter which side I call Side a and which Side b?
No — subtracting both from the same total gives an identical result regardless of which known length is entered into Side a and which into Side b, since perimeter minus a minus b equals perimeter minus b minus a either way.
Can two different triangles share the same missing length?
Yes, easily — a perimeter of 12 with sides 3 and 4, a perimeter of 15 with sides 5 and 5, and a perimeter of 20 with sides 7 and 8 all return a missing length of exactly 5, even though the three triangles differ completely in shape and total size.