Question

Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AD = 12

and AC = 15, what is the length of AB in simplest radical form?

Answer 1

In a right triangle ABC with altitude BD drawn to hypotenuse AC, if AD = 12 and AC = 15, we can use the Pythagorean theorem to find the length of AB. The length of AB is √135 in simplest radical form.

Step-by-step explanation:

In a right triangle ABC with altitude BD drawn to hypotenuse AC, if AD = 12 and AC = 15, we can use the Pythagorean theorem to find the length of AB. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Using the theorem, we have: AB2 = AD2 + BD2

Substituting the given values, AB2 = 122 + BD2

Since BD is the altitude drawn to hypotenuse AC, it divides AC into two segments: AD and CD. Therefore, CD = AC - AD = 15 - 12 = 3.

Now, we have a right triangle BCD, where BC is the hypotenuse, BD is the altitude, and CD is the base. We can use the Pythagorean theorem on this triangle to find BD:

BD2 = BC2 - CD2

Substituting the values, BD2 = AB2 - CD2 = 144 - 9 = 135

Taking the square root of both sides, BD = √135

Answer 2

x = 6

Step-by-step explanation:

let 'x' = BD

x/3 = 12/x

x² = 36

x =
`√(36)`

x = 6