Question

geometry with statistics honors - ferraro - 2 - a topic 4: readiness assessment what is the length of side b? a. 169 b. 43 c. 13 d. 12

Explanation:

Step1: Consider right - triangle ADC

In right - triangle ADC, we know the height \(CD = 5\) and half of the base \(AD=\frac{24}{2}=12\).

Step2: Apply Pythagorean theorem

The Pythagorean theorem states that for a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(c=\sqrt{a^{2}+b^{2}}\). In right - triangle ADC, \(b=\sqrt{AD^{2}+CD^{2}}\).
Substitute \(AD = 12\) and \(CD = 5\) into the formula: \(b=\sqrt{12^{2}+5^{2}}=\sqrt{144 + 25}=\sqrt{169}=13\).

Answer:

C. 13