Question

Find the value of x. Please help! Thanks.

Answer 1

`\huge\boxed{x=√(30)}`

Explanation:

ΔABC and ΔBDC are similar (AAA).

Therefore the corresponding sides are in proportion:

`(AC)/(BC)=(BC)/(CD)`

substitute

`AC=7+3=10\\{BC}=x\\CD=3`

`(10)/(x)=(x)/(3)` cross multiply

`(10)(3)=(x)(x)\\\\30=x^2\\\\x^2=30\to x=√(30)`