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4 years ago

Find the length of CD.

Mathematics

1 answer:

aliina [53]4 years ago

8 0

Answer:

The answer to your question is CD = 4

Step-by-step explanation:

Data

AD = 8

BD = 2

CD = ?

Process

Use proportions to solve this problem. Compare triangle ACD and triangle CDB.

Large triangle CD/AD

Small triangle BD/CD

Equal both proportions

CD/BD = AD/CD

-Solve for CD

CD² = AD x BD

-Substitution

CD² = 8 x 2

-Simplification

CD² = 16

-Result

CD = 4

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What are the values of a and b

makvit [3.9K]

Answer:

$\large\boxed{B.\ a=8,\ b=4\sqrt5}$

Step-by-step explanation:

We have three similar triangles:

$\triangle ABC\sim\triangle DBA\sim\triangle DAC$

therefore the sides are in proportion:

$\dfrac{AD}{CD}=\dfrac{BD}{AD}$

We have AD = a, CD = 16 and BD = 4. Substitute:

$\dfrac{a}{16}=\dfrac{4}{a}$ <em>cross multiply</em>

$(a)(a)=(16)(4)\\\\a^2=64\to a=\sqrt{64}\\\\a=8$

and other proportion:

$\dfrac{AB}{BC}=\dfrac{BD}{AB}$

We have AB = b, BC = 16 + 4 = 20 and BD = 4. Substitute:

$\dfrac{b}{20}=\dfrac{4}{b}$ <em>cross multiply</em>

$(b)(b)=(20)(4)\\\\b^2=80\to b=\sqrt{80}\\\\b=\sqrt{16\cdot5}\\\\b=\sqrt{16}\cdot\sqrt{5}\\\\b=4\sqrt{5}$

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