Question

Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AC =11 and DC=5 what is the length of BC in the simplest radical form

Answer 1

`The`
`length`
`of`
`BC`
`is`
`√(55)`
`(units)`.

Explanation:

Given ABC is a right triangle.

AC is the hypotenuse and BD is the altitude.

AB and BC are legs of the triangle ABC.

AC = 11 and DC = 5

Leg rule of geometric mean theorem:

`(hypotenuse)/(leg)=(leg)/(part)`

`(AC)/(BC)=(BC)/(DC)`

`(11)/(x)=(x)/(5)`

Do cross multiplication.

`11 * 5= x*x`

`55=x^(2)`

Taking square root on both sides.

`√(55) =\sqrt{x^(2) }`

`√(55)=x`,
`since`
`√(55)`
`cannot`
`be`
`reduced.`

The length of BC is
`√(55)`.