Question

24.) a=???, b= 4, c= 4√5

Explanation:

Assuming this is a right - triangle problem with \(c\) as the hypotenuse and \(a\), \(b\) as the legs, we use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\).

Step 1: Substitute the known values

We know that \(b = 4\) and \(c=4\sqrt{5}\). Substitute these values into the Pythagorean theorem: \(a^{2}+4^{2}=(4\sqrt{5})^{2}\)

Step 2: Simplify the equation

First, calculate \(4^{2}=16\) and \((4\sqrt{5})^{2}=4^{2}\times(\sqrt{5})^{2}=16\times5 = 80\). So the equation becomes \(a^{2}+16 = 80\)

Step 3: Solve for \(a^{2}\)

Subtract 16 from both sides of the equation: \(a^{2}=80 - 16=64\)

Step 4: Solve for \(a\)

Take the square root of both sides. Since \(a\) represents a length (in the context of a triangle side), we take the positive square root. So \(a=\sqrt{64} = 8\)

Answer:

\(a = 8\)