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Aleksandr [31]
4 years ago
14

Answers are A:4 square root 5 B:16 C:6 D:8 square root 5

Mathematics
1 answer:
julia-pushkina [17]4 years ago
5 0

Answer:

\large\boxed{A:\ 4\sqrt5}

Step-by-step explanation:

<em>Look at the picture.</em>

ΔABC and ΔADB are similar. The corresponding angles are in proportion:

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

We have:

AB=x,\ AC=5+11=16,\ AD=5

Substitute:

\dfrac{x}{16}=\dfrac{5}{x}                 <em>cross multiply</em>

x^2=(16)(5)\to x=\sqrt{(16)(5)}         <em>use √ab = √a · √b</em>

x=\sqrt{16}\cdot\sqrt5\\\\x=4\sqrt5

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