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rosijanka [135]
2 years ago
9

What are the values of a and b​

Mathematics
1 answer:
Westkost [7]2 years ago
3 0

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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