Question

THIRD TIME ASKING FOR HELP PLEASE HELP ME!!!!!!!!!!!!!!!!!!!

Answer 1

Answer:  9 units

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Explanation:

For now, focus on triangle ABD. This is a right triangle due to BD being an altitude.

Use the pythagorean theorem to find that...

(AD)^2 + (BD)^2 = (AB)^2

(1)^2 + (BD)^2 = (3)^2

1 + (BD)^2 = 9

(BD)^2 = 9-1

(BD)^2 = 8

Normally we would isolate BD itself, but I'll stop short and use that last line instead.

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The triangles ABD and BCD are similar triangles (we can prove this using the AA similarity theorem).

Since we have similar triangles, we can form the proportion shown below

AD/BD = BD/CD

This cross multiplies to

AD*CD = (BD)^2

We know that AD = 1 and (BD)^2 = 8, so,

AD*CD = (BD)^2

1*CD = 8

CD = 8

This then means,

x = CD+DA

x = 8+1

x = 9

AC is 9 units long.