Question

one leg of a right - triangle has a length of 43.2 millimeters. the hypotenuse of the triangle has a length of 196.8 millimeters. what is the length of the other leg of the triangle, in millimeters?
a) 43.2
b) 120
c) 212
d) 201.5

Explanation:

Step1: Apply Pythagorean theorem

Let \(a = 43.2\), \(c=196.8\), and we want to find \(b\). The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), so \(b^{2}=c^{2}-a^{2}\).

Step2: Substitute values

\(b^{2}=(196.8)^{2}-(43.2)^{2}\). Using the difference - of - squares formula \(x^{2}-y^{2}=(x + y)(x - y)\), where \(x = 196.8\) and \(y = 43.2\), we have \(b^{2}=(196.8 + 43.2)(196.8-43.2)=(240)\times(153.6)\).

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

\(b^{2}=240\times153.6 = 36864\).

Step4: Find \(b\)

\(b=\sqrt{36864}=192\).

Answer:

C. 192