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16-03-2021
Mathematics

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Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AB=8 and AD=4, what is the length of AC?

Given right triangle ABC with altitude BD drawn to hypotenuse AC If AB8 and AD4 what is the length of AC class=

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16-03-2021

Answer:

AC = 16

Step-by-step explanation:

In ΔABC & ΔABD

angle ABC = angle ADB ---- (each 90°)

angle BAD = angle CAB ---- (common)

so, therefore

ΔABC ~ ΔABD --- (by AA similarity)

by similarity in ΔABC & ΔABD

AB/AC = AD/AB

8/AC = 4/8

AC = 8×8÷4

AC = 16

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