Question

1. find the value of x. show your work for full credit!!!

Explanation:

Step1: Apply the Pythagorean theorem in right - triangle ABD and BCD

Since \(\triangle ABD\) and \(\triangle BCD\) are right - triangles and \(AB = BC=21\), in right - triangle \(ABD\), \(AB^{2}=AD^{2}+BD^{2}\), and in right - triangle \(BCD\), \(BC^{2}=CD^{2}+BD^{2}\). Because \(AB = BC\), we have \(AD = CD\).

Step2: Set up an equation for \(x\)

We know that \(AD=x - 8\) and \(CD = 16\). Since \(AD = CD\), we can set up the equation \(x-8=16\).

Step3: Solve the equation for \(x\)

Add 8 to both sides of the equation \(x-8=16\). We get \(x=16 + 8\).

Answer:

\(x = 24\)