Q&A for How to Find the Perimeter of a Triangle

If you know only 1 side but all 3 angles, you can use the rule of sines to find the remaining sides, then calculate the perimeter. If you know 1 side and 1 angle, you won’t be able to find the perimeter unless you’re dealing with a right triangle. For right triangles, you know that 1 angle is always 90°, so if you know another angle, you can use the sum of angles (180°) to figure out the third one. From there, you can use the laws of sine and cosine to figure out the other sides.

If it’s a right triangle, you can use the Pythagorean theorem (a2 + b2 = c2) to find the length of the missing side. From there, you can easily calculate the perimeter. For other types of triangles, you can use the law of cosines to find the perimeter if you know 2 sides and at least 1 of the angles.

Since the perimeter is the sum of the lengths of all sides, you can solve for the missing side by subtracting the lengths of the other 2 sides from the perimeter.

No. You can know the exact shape of the triangle from the angles but nothing about its size, so the perimeter could be anything. (At least for Euclidean geometry; in spherical geometry, all similar triangles are congruent so you do know the scale and thus the perimeter.)

Triangle inequality says no side can be longer than the sum of the other two. If the third side were 14 cm, it would make a line segment, not a triangle, but the next integer smaller 13 cm works. That makes a perimeter of 27 cm.

Subtract 4/3 from 42/15, then divide by 2.

You can't find the perimeter with just the base and height because you need the measure of at least two sides and an angle between them.

It depends on where the angle is situated in relation to the two sides.

If you know all three side lengths, that's all you need. Add the three sides together. The height is not needed.

The triangle inequality means the third side must be between 4 and 30cm, so the perimeter is between 34 and 60 cm.

Calculate the length of each side using the Pythagorean theorem, and add them together.

Set up three equations in three unknowns: a + b + c = 74; a = (b + c) - 6; and c = a - 4. Solve by substitution, such as substituting (a - 4) for c in the first two equations and solving those two simultaneously.

You'd also need to know the angle between the sides.

If all you know is the area, it's not possible to find the perimeter.

This triangle is isosceles, because the third angle is also 45°. (180° - 90° - 45° = 45°.) The Pythagorean theorem (a² + b² = c²) tells us that the sum of the squares of the two legs of a right triangle equals the square of the hypotenuse. Since in this triangle a=b, a² + a² = 2a² = c². The hypotenuse is given as 25, so c²=625. Therefore, 2a² = 625. Then a²=312.5, and a=17.67. That's what b equals, too. So the perimeter is 25 + 17.67 + 17.67 = 60.34.

The lengths of the rectangle's four sides are in the ratio of 4:7:4:7. Add those four numbers together to get 22. 66÷22 = 3. Multiply 3 by the four-side ratio to get the actual side lengths of 12, 21, 12 and 21 units. The rectangle's area is (12)(21) = 252 square units.

Perimeter of a triangle and its area are not correlated, they are entirely different quantities. You cannot find one from the other without some more information about the triangle.

It can't be done. The third side would be either 8 or 17, but we don't know which.

Let's assume you're referring to a rectangle. Let w be the width and (w+3) be the length. Then w + w + (w+3) + (w+3) = 38. So 2w + 2(w+3) = 2w + (2w + 6) = 4w + 6 = 38. Then 4w = 32, and w = 8. So the width is 8.

If all you know is the area, you don't have enough information to find the perimeter. That's because with a given area, the base could be many different lengths.

See Find the Distance Between Two Points . Use that technique to find the distance between each pair of points. Then add the three distances together.

If you're talking about an equilateral triangle, the perimeter is three times the side length, which means in this case 3(x + 3) = 3x + 9.

See Learn Trigonometry and related articles.

You would first have to know whether the 4.9 side is the hypotenuse or one of the legs. The ratio of the sides of a triangle with those angles is 1:1:√2. So you would use that ratio and the 4.9 dimension to calculate the other two sides and then the perimeter.

Multiply it by 3/5 and 4/5 to find the other sides, then add all three together.

Simply add the lengths of the sides together to find the perimeter.

If by "sides" you mean two or three sides of the given triangle, then it isn't possible to find them with only the perimeter, (unless it is an isosceles triangle). You need to know at least two sides or angles (depending on the number of sides you need to find) in order to use perimeter and find the unknown side(s). As for an isosceles triangle, since all the three sides are the same length, you can write the perimeter formula as; perimeter = 3*x (x being the sides) calculate x and there you have all three sides of the that triangle. If you want, you can double check your answer by checking if 3*x = perimeter, or not.

You can't. The formula for a triangle's perimeter is 3*sides, or more commonly written as A+B+C (they are the same thing). If all you know is the hypotenuse, you can't find the perimeter of the triangle; neither directly with the above formula, nor indirectly with the Pythagorean theorem. You need to know at least one more side or 2 angles.

The Pythagorean theorem is itself a proof that the triangle in question is a right triangle. The square of a right triangle's longest side i.e the hypotenuse - denoted by "c" - is always equal to the sum of the squares of the other two sides. Using Pythagorean theorem, you can easily proof that the said triangle is right or not. c^2 (hypotenuse) = a^2 (base) + b^2 (perpendicular).

S + (S + 12) + (S x 2) = 52. So 4S + 12 = 52, 4S = 40, and S = 10. So the shortest side is 10 m, another side is 10 + 12 = 22 m, and the third side is 2S = 20 m. The perimeter is 10 + 22 + 20 = 52 m.