Find the value of x.

Mathematics

1 answer:

lawyer [7]4 years ago

4 0

Answer:

$\huge\boxed{x=\sqrt{70}}$

Step-by-step explanation:

ΔABC and ΔADB are similar (AAA).

Therefore the corresponging sides are in proportion:

$\dfrac{AB}{AD}=\dfrac{AC}{AB}$

Substitute:

$AB=x\\AC=7+3=10\\AD=7$

$\dfrac{x}{7}=\dfrac{10}{x}$ <em>cross multiply</em>

$(x)(x)=(7)(10)\\\\x^2=70\to x=\sqrt{70}$

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