To find the length of the hypotenuse of a right triangle when the lengths of the two legs are known, we can use the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The formula can be written as:
c² = a² + b²
In this case, the lengths of the legs are:
- a = 4 units
- b = 5 units
Now, we can plug in the values into the Pythagorean theorem:
c² = 4² + 5²
This simplifies to:
c² = 16 + 25
c² = 41
To find the hypotenuse (c), we take the square root of both sides:
c = √41
Calculating the square root gives us:
c ≈ 6.4 units
Therefore, the length of the hypotenuse of the right triangle with legs measuring 4 and 5 units is approximately 6.4 units.