Question

Find the value of x. Please help! Thanks.

Answer 1

Answer:

$\huge\boxed{x=\sqrt{30}}$

Step-by-step explanation:

ΔABC and ΔBDC are similar (AAA).

Therefore the corresponding sides are in proportion:

$\dfrac{AC}{BC}=\dfrac{BC}{CD}$

substitute

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

$\dfrac{10}{x}=\dfrac{x}{3}$           cross multiply

$(10)(3)=(x)(x)\\\\30=x^2\\\\x^2=30\to x=\sqrt{30}$