Question

for items 7 - 10, use the figure shown. 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 that the perpendicular from C to AB is CD = 5 and AD is half of the base (assuming the triangle is isosceles with respect to the perpendicular from C to AB, since no other information about non - symmetry is given). Let's assume the base AB = 24, so AD=12.

Step2: Apply the Pythagorean theorem

In right - triangle ADC, by the Pythagorean theorem \(b^{2}=AD^{2}+CD^{2}\). Here, \(AD = 12\) and \(CD = 5\). So \(b=\sqrt{12^{2}+5^{2}}\).

Step3: Calculate the value of b

\(b=\sqrt{144 + 25}=\sqrt{169}=13\).

Answer:

C. 13