Question

Please explain it. and no links. thanks.

Answer 1

Answer:  4*sqrt(66)

This is the same as saying $4\sqrt{66}$

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Explanation:

x = length of segment BD

Because BD is an altitude of triangle ABC, this means the triangle is split into two smaller right triangles which are similar to the original. All three right triangles are similar to one another.

What this leads to is the proportion

CD/BD = BD/AD

Apply substitution and solve for x.

24/x = x/44

24*44 = x*x .... cross multiply

1056 = x^2

x = sqrt(1056)

x = sqrt(16*66)

x = sqrt(16)*sqrt(66)

x = 4*sqrt(66)

Notice how I factored 1056 in such a way that I pulled out the largest perfect square factor (16). Then I used the rule $\sqrt{x*y} = \sqrt{x}*\sqrt{y}$ to break up the root.