Question

finding the length of a hypotenuse
consider the triangle.
find the length of the hypotenuse, c.
the length of the hypotenuse is cm.

Explanation:

Step1: Apply Pythagorean theorem

The Pythagorean theorem states that for a right - triangle \(a^{2}+b^{2}=c^{2}\), where \(a = 24\) cm, \(b = 10\) cm and \(c\) is the hypotenuse.
So, \(c^{2}=24^{2}+10^{2}\).

Step2: Calculate \(24^{2}\) and \(10^{2}\)

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

Step3: Sum the values

\(c^{2}=676\).

Step4: Find \(c\)

Take the square root of \(c^{2}\), \(c=\sqrt{676}\).
Since \(26\times26 = 676\), \(c = 26\).

Answer:

\(26\)