Question

What is the value of x in the diagram below? Id necessary, round your answer to the nearest tenth of a unit.

Answer 1

D

Explanation:

This uses the Altitude- on- Hypotenuse theorem

An altitude drawn to the hypotenuse of a right triangle.

The 2 triangles formed are similar to the given triangle and each other, thus

Δ BAC ~ Δ BDA

The ratios of corresponding sides are equal, that is

`(BA)/(BD)` =
`(BC)/(BA)` , substitute values

`(14)/(x)` =
`(30)/(14)` ( cross- multiply )

30x = 196 ( divide both sides by 30 )

x ≈ 6.5 ( to the nearest tenth ) → D