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THIRD TIME ASKING FOR HELP PLEASE HELP ME!!!!!!!!!!!!!!!!!!!
Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AB=3 and AD=1, what is the length of AC?

THIRD TIME ASKING FOR HELP PLEASE HELP ME Given Right Triangle ABC With Altitude BD Drawn To Hypotenuse AC If AB3 And AD1 What Is The Length Of AC class=

Sagot :

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.

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