Solve for X A: 12.5 B: 5 C: 6[tex]\sqrt{3}[/tex] D:12

2 answers
Question:

Solve for X
A: 12.5
B: 5
C: 6[tex]\sqrt{3}[/tex]
D:12

Answers

Answer:D. 12Step-by-step explanation:(LOOK AT THE PICTURE)ΔADC and ΔCDB are similar (AAA). Therefore the corresponding sides are in proportion:[tex]\dfrac{AD}{CD}=\dfrac{CD}{DB}[/tex]We have[tex]AD=16,\ CD=x,\ DB=9[/tex]Substitute:[tex]\dfrac{16}{x}=\dfrac{x}{9}[/tex]          cross multiply[tex]x^2=(9)(16)\to x=\sqrt{(9)(16)}\\\\x=(\sqrt9)(\sqrt{16})\\\\x=(3)(4)\\\\x=12[/tex]

bear in mind that, a perpendicular line stemming from the right-angle like so, creates three similar triangles, a large one, containing the other two smaller ones, a medium and a small.so.. .we can just use the medium and small proportions.Check the picture below.

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