Question

Please help!!

Find the value of x.

X=

Answer 1

x =
`√(21)`

Explanation:

Δ BCD and Δ ABD are similar thus the ratios of corresponding sides are equal, that is

`(BD)/(AD)` =
`(CD)/(BD)` , substitute values

`(x)/(7)` =
`(3)/(x)` ( cross- multiply )

x² = 21 ( take the square root of both sides )

x =
`√(21)`

Answer 2

Explanation:

Hello,

We can write three equations thanks to Pythagoras

`AB^2+AC^2=(7+3)^2\\x^2+7^2=AB^2\\x^2+3^2=BC^2\\`

So it comes

`x^2+7^2+x^2+3^2=(7+3)^2\\\\2x^2=100-49-9=42\\\\x^2 = 42/2=21\\\\x = \sqrt{\boxed{21}}\\`

Hope this helps