Understanding Triangle Side Ratios
A triangle's sides can be expressed as a ratio, such as 3:4:5. To find the actual side lengths, you multiply each ratio part by a common scale factor k. The scale factor can be determined if you know either the perimeter or the length of one specific side.
How It Works
From Perimeter
Divide the perimeter by the sum of ratio parts to find k.
k = P / (r1 + r2 + r3)
From One Side
Divide the known side length by its corresponding ratio part.
k = side / ratio_part
Actual Sides
Multiply each ratio part by the scale factor k.
a = k x r1, b = k x r2, c = k x r3
Common Triangle Ratios
- 3:4:5 - The classic Pythagorean triple (right triangle).
- 5:12:13 - Another Pythagorean triple.
- 1:1:1 - Equilateral triangle.
- 1:1:sqrt(2) - Isosceles right triangle (45-45-90).
- 1:sqrt(3):2 - 30-60-90 triangle.
Triangle Inequality Check
Not all ratios form valid triangles. The ratio parts must satisfy the triangle inequality: the sum of any two parts must be greater than the third. For example, 1:2:4 does not form a valid triangle because 1 + 2 = 3, which is less than 4.