Question

What is the value of x

Answer 1

x = 5

Explanation:

This uses the altitude on hypotenuse theorem

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

Δ ADB ~ Δ BDC

Since the triangles are similar then the ratios of corresponding sides are equal, that is

`(DB)/(DC)` =
`(AD)/(BD)` , substitute values

`(10)/(4x)` =
`(x)/(10)` ( cross- multiply )

4x² = 100 ( divide both sides by 4 )

x² = 25 ( take the square root of both sides )

x =
`√(25)` = 5