Question

a right triangle and two of its side lengths are shown in the diagram. which measurement is closest to the value of b? 22.5 cm 16 cm 23.7 cm 28.4 cm

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Here, \(c = 24\) cm and \(a = 4\) cm, and we want to find \(b\). So, \(b=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute values

Substitute \(c = 24\) and \(a = 4\) into the formula: \(b=\sqrt{24^{2}-4^{2}}=\sqrt{(24 + 4)(24 - 4)}=\sqrt{28\times20}=\sqrt{560}\).

Step3: Calculate the square - root

\(\sqrt{560}\approx23.7\) cm.

Answer:

23.7 cm