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3 years ago

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

Mathematics

1 answer:

julia-pushkina [17]3 years ago

5 0

Answer:

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

Step-by-step explanation:

Look at the picture.

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:

$\dfrac{x}{16}=\dfrac{5}{x}$ cross multiply

$x^2=(16)(5)\to x=\sqrt{(16)(5)}$ use √ab = √a · √b

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

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Explanation:

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To determine the value of x, let us simplify the equation.

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Simplifying, we get,

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$x=3.86$

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