Question

1. if bc = 4 and cd = 27, find ac.

31
6√3
108
√31

Explanation:

Step1: Apply geometric - mean theorem

In right - triangle ABD with altitude AC, we have $AC^{2}=BC\times CD$.

Step2: Substitute given values

Given $BC = 4$ and $CD=27$, then $AC^{2}=4\times27 = 108$.

Step3: Solve for AC

$AC=\sqrt{108}=\sqrt{36\times3}=6\sqrt{3}$.

Answer:

$6\sqrt{3}$