Question

in the right triangle shown below, what is the length of the missing side length labeled x?
23
24
√423
√509

Explanation:

Step1: Apply the Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Here, \(c = 25\), \(a=7\), and \(b = x\). So, \(7^{2}+x^{2}=25^{2}\).

Step2: Simplify the equation

\(49+x^{2}=625\). Then, \(x^{2}=625 - 49\).

Step3: Calculate \(x^{2}\)

\(x^{2}=576\).

Step4: Solve for \(x\)

Take the square root of both sides, \(x=\sqrt{576}\). Since \(x>0\) (length), \(x = 24\).

Answer:

24