Question

a right triangle and two of its side lengths are shown in the diagram. which measurement is closest to the value of w? 379 mm 37 mm 94.8 mm 9,604 mm

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Here, \(c = 98\) mm, \(a = 25\) mm and \(b=W\). So, \(W=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute values

\(W=\sqrt{98^{2}-25^{2}}=\sqrt{(98 + 25)(98 - 25)}\) (using \(x^{2}-y^{2}=(x + y)(x - y)\)). First, \(98+25 = 123\) and \(98 - 25=73\). Then \(W=\sqrt{123\times73}=\sqrt{8979}\approx94.8\) mm.

Answer:

94.8 mm