Question

Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AD = 10 and AC = 45, what is the length of AB in simplest radical form?

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Answer 1

Explanation:

In a right triangle with altitude drawn to the hypotenuse, the length of the altitude divides the hypotenuse into two segments proportional to the lengths of the segments adjacent to the altitude.

Let's denote the length of AB as x. According to the given information:

AD = 10

AC = 45

Using the property of similar triangles, we can set up the following proportion:

AB/AD = AC/AB

Substituting the given values:

x/10 = 45/x

To solve for x, we can cross-multiply:

x^2 = 10 * 45

x^2 = 450

Taking the square root of both sides:

x = √450

Simplifying the radical:

x = √(9 * 50)

x = √(9) * √(50)

x = 3√(50)

Therefore, the length of AB in simplest radical form is 3√(50).