Question

topic: the pythagorean theorem
progress:
question id: 1188574
the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer
find the length of the hypotenuse, side c, of a right triangle with legs of length a = 4 and b = 5. use a calculator to estimate the square root to one decimal place.
the length of the hypotenuse, c, is approximately ______

Explanation:

Step1: Apply Pythagorean theorem

$$c^{2}=a^{2}+b^{2}$$
Substitute \(a = 4\) and \(b = 5\) into the formula:
$$c^{2}=4^{2}+5^{2}$$
$$c^{2}=16 + 25$$
$$c^{2}=41$$

Step2: Solve for \(c\)

Take the square root of both sides:
$$c=\sqrt{41}$$
Using a calculator, \(\sqrt{41}\approx6.4\)

Answer:

\(6.4\)