Question

Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AB = 3 and AC = 9, what is the length of AD? (Note: the figure is not drawn to scale.)

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Answer 1

The length of AD is 1 unit

Explanation:

Let us solve the question

In Δ ABC

∵ ∠B is a right angle

∵ BD is perpendicular to the hypotenuse AC

∴ (AB)² = AD × AC ⇒ rule

∵ AB = 3 units

∵ AC = 9 units

∵ AD = x

→ Substitute them in the rule above

∴ (3)² = x × 9

∴ 9 = 9x

→ Divide both sides by 9

∵
`(9)/(9)` =
`(9x)/(9)`

∴ 1 = x

∴ The length of AD is 1 unit