Question

if a right triangle has legs measuring 10 cm and 24 cm, how long is the hypotenuse? (1 point)

cm

check answer remaining attempts : 3

Explanation:

Step1: Apply the Pythagorean theorem

For a right - triangle with legs \(a = 10\) and \(b = 24\), and hypotenuse \(c\), the Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\). So, \(c^{2}=10^{2}+24^{2}\).

Step2: Calculate \(a^{2}\) and \(b^{2}\)

\(10^{2}=10\times10 = 100\), \(24^{2}=24\times24=576\). Then \(c^{2}=100 + 576\).

Step3: Sum the values

\(c^{2}=100+576=676\).

Step4: Find \(c\)

Take the square root of \(c^{2}\). Since \(c>0\) (length of a side), \(c=\sqrt{676}\). And \(\sqrt{676} = 26\).

Answer:

\(26\)