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17 votes
Given right triangle ABC with altitude BD drawn to hypotenuse AC. If

AD = 6 and AC = 24, what is the length of AB?

User Lyana
by
6.3k points

1 Answer

11 votes

Explanation:

AC = 24 and AD = 6.

that means that DC = 24 - 6 = 18

the height of a right-angled triangle to the Hypotenuse is the square root of the product of the lengths of the 2 Hypotenuse segments.

in our case

BD = sqrt(AD × DC) = sqrt(6 × 18) = sqrt(108)

but this height is also creating another right-angled triangle with the first Hypotenuse segment (AD) and the side AB.

and we can use Pythagoras to calculate AB :

AB² = BD² + AD² = 108 + 6² = 108 + 36 = 144

AB = sqrt(144) = 12

User Dagoof
by
6.8k points
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