Question

for items 7 - 10, use the figure shown. what is the length of side a? a 169 b 43 c 13 d 12

Explanation:

Step1: Consider right - triangle BCD

In right - triangle BCD, we know the height \(CD = 5\) and half of the base \(BD=\frac{24}{2}=12\) (assuming the triangle is isosceles with respect to the perpendicular from \(C\) to \(AB\)).

Step2: Apply Pythagorean theorem

The Pythagorean theorem states that for a right - triangle with legs \(x\) and \(y\) and hypotenuse \(z\), \(z=\sqrt{x^{2}+y^{2}}\). In right - triangle BCD, \(a=\sqrt{5^{2}+12^{2}}\).
\[a=\sqrt{25 + 144}=\sqrt{169}=13\]

Answer:

C. 13