Perimeter: Right-angled Triangle
Learn and practice calculating the perimeter of right-angled triangles using the Pythagorean theorem.
Right-angled Triangle
Use the workspace below. Write equations like P = 24 to solve for the perimeter.
📖 Perimeter Study Guide
3. Right-angled Triangle Perimeter
For a right-angled triangle with perpendicular legs and , we can use the Pythagorean theorem () to find the hypotenuse , and then calculate the perimeter.
Variables:
• = Perimeter
• = first perpendicular leg
• = second perpendicular leg
• = hypotenuse
Derivation:
1. The perimeter of any triangle is the sum of its three sides: .
2. For a right-angled triangle, if the hypotenuse is unknown, calculate it using the Pythagorean theorem: .
3. Substitute back to find the perimeter.
Frequently Asked Questions
What is perimeter?
Perimeter is the total boundary of a two-dimensional shape. It includes both the outer boundary and any inner boundaries (like the edges of holes inside the shape).
How do you calculate the perimeter of a rectangle?
The perimeter of a rectangle is the sum of all its four sides: P = 2w + 2h or P = 2(w + h), where w is the width and h is the height.
Why is a square's perimeter formula P = 4s?
A square is a special case of a rectangle where width and height are equal (w = h = s). Substituting this into the rectangle formula gives P = 2(s + s) = 4s.
How does a hole affect the perimeter?
Since perimeter measures the entire boundary of a shape, a hole adds to the perimeter. The total perimeter is the outer perimeter plus the inner perimeter (the perimeter of the hole).
How do you find the perimeter of a right-angled triangle if one side is missing?
Since we've already learned the Pythagorean theorem (a² + b² = c²), we can calculate the missing side length first and then sum all three sides together to get the perimeter.