Question

one leg of a right triangle has a length of 12.6 millimeters. the hypotenuse of the triangle has a length of 57.4 millimeters. what is the length of the other leg of the triangle, in millimeters?
a 12.6
b 35
c 56
d 58.8

Explanation:

Step1: Apply Pythagorean theorem

Let \(a = 12.6\), \(c=57.4\), and \(b\) be the unknown leg. The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), so \(b^{2}=c^{2}-a^{2}\).

Step2: Substitute values

\(b^{2}=57.4^{2}-12.6^{2}\). Using the difference - of - squares formula \(x^{2}-y^{2}=(x + y)(x - y)\), here \(x = 57.4\), \(y = 12.6\). Then \(b^{2}=(57.4 + 12.6)(57.4-12.6)\).
\(b^{2}=(70)(44.8)\)
\(b^{2}=3136\)

Step3: Solve for \(b\)

Take the square root of both sides: \(b=\sqrt{3136}\)
\(b = 56\)

Answer:

C. 56