To find the length of the hypotenuse of a right-angled triangle, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. The formula is:
c² = a² + b²
where
c is the length of the hypotenuse,
a is the length of one of the other sides (base),
and b is the length of the other side (height).
Given:
a = 5 cm (base)
b = 11 cm (height)
We are trying to find c (hypotenuse).
Using the formula, we substitute the given values:
c² = a² + b²
c² = (5 cm)² + (11 cm)²
c² = 25 cm² + 121 cm²
c² = 146 cm²
To find the length of the hypotenuse (c), we take the square root of both sides of the equation:
c = √146 cm²
Now, use a calculator or perform the square root calculation manually to find the value of c:
c ≈ 12.08 cm
Therefore, the length of the hypotenuse of the right-angled triangle is approximately 12.08 cm.
