3 4 5 Triangle
3 4 5 Triangle Calculator
Scale a 3 4 5 right triangle and find sides, area, and perimeter.
Calculator Mode
Scale 3-4-5 Triangle
Result
Formula:
The 3 4 5 triangle is the smallest and most well-known Pythagorean triple. Its sides follow the ratio 3 : 4 : 5, and it always forms a perfect right angle. Builders, carpenters, and surveyors have relied on this pattern for centuries to create square corners without any special tools.
This calculator lets you scale the 3 4 5 triangle by any factor you choose. Enter a scale factor k, and the calculator will multiply each side by that value. It also computes the area and perimeter of the scaled triangle with full step-by-step math.
Enter a positive scale factor k. The calculator multiplies 3, 4, and 5 by that factor and computes the resulting area and perimeter.
Formula
The 3 4 5 triangle uses the simplest Pythagorean triple. You can scale every side by the same factor k to create a larger or smaller version that is still a right triangle. The ratio between the sides stays the same no matter what value of k you use.
After scaling, the area is half the product of the two legs, and the perimeter is the sum of all three sides. Because the ratio never changes, a 3 4 5 triangle at any scale always has the same angles.
Triangle Diagram
Triangle Diagram Key
- The base ratio is 3 : 4 : 5.
- Side a = 3k is the shorter leg.
- Side b = 4k is the longer leg.
- Side c = 5k is the hypotenuse — always the longest side.
- Multiply all three sides by the same k to keep the right angle.
How to Use This Calculator
- Enter a scale factor k in the input field.
- Click Calculate to see the scaled side lengths, area, and perimeter.
- Review the step-by-step solution below the result.
- Try different values of k to compare triangle sizes.
- Click Reset to clear the input and start fresh.
Step-by-Step Examples
Example 1: Scale factor k = 2
Example 2: Scale factor k = 5
Example 3: Scale factor k = 0.5
What the Result Means
The calculator gives you five values: the three scaled sides, the area, and the perimeter. Side a is always the shorter leg (3k), side b is the longer leg (4k), and c is the hypotenuse (5k).
The area tells you the space inside the triangle in square units. The perimeter gives you the total length around the outside. Both values grow as you increase k, but the triangle always keeps its right angle.
Side Ratio
The side ratio for every 3 4 5 triangle is 3 : 4 : 5.
A scaled version keeps the same ratio as 3k : 4k : 5k, so the hypotenuse is always the side matched with 5k.
When to Use This Calculator
- Checking a right angle in construction by measuring 3, 6, or 9 feet along one side and 4, 8, or 12 feet along another.
- Solving geometry homework that involves 3 4 5 triangle scaling.
- Designing layouts or floor plans that require exact 90-degree corners.
- Quickly estimating areas and perimeters without a full right triangle solver.
- Teaching students how scaling preserves angles in similar triangles.
Common Mistakes
- Scaling only one or two sides instead of all three: all sides must be multiplied by the same k.
- Treating 5 as a leg instead of the hypotenuse: 5 is always the longest side.
- Thinking only exact values of 3, 4, 5 work: any multiple like 6, 8, 10 or 15, 20, 25 is also valid.
- Mixing up area and perimeter formulas: area uses multiplication and division by 2, perimeter uses addition.
- Using a negative or zero scale factor: k must be greater than 0.
FAQs
Answers to the most common right-triangle solving questions.
01 What is the 3 4 5 triangle rule? expand_more
The 3 4 5 rule states that a triangle with sides in the ratio 3 : 4 : 5 always forms a right angle. This works because 3² + 4² = 9 + 16 = 25 = 5², satisfying the Pythagorean theorem.
02 How do I scale a 3 4 5 triangle? expand_more
Multiply all three sides by the same factor k. For example, with k = 3, the sides become 9, 12, and 15. The triangle stays a right triangle as long as you scale every side equally.
03 What is the area of a 3 4 5 triangle? expand_more
The base 3 4 5 triangle has an area of (3 × 4) / 2 = 6 square units. For a scaled version, use Area = (3k × 4k) / 2.
04 Is 6, 8, 10 a 3 4 5 triangle? expand_more
Yes. Dividing each side by 2 gives 3, 4, 5. So 6, 8, 10 is a 3 4 5 triangle scaled by k = 2.
05 Can I use the 3 4 5 rule to check a right angle? expand_more
Yes. Measure 3 units along one side and 4 units along the other. If the diagonal between those endpoints measures exactly 5 units, the corner is a right angle.
06 What is the perimeter of a 3 4 5 triangle? expand_more
The base perimeter is 3 + 4 + 5 = 12 units. For any scaled version, the perimeter is 12k, where k is the scale factor.