5.05 dilutions assessment usatestprep

answer:

c

step-by-step explanation:

calculate ac using pythagoras' identity in δabc

ac² = 20² - 12² = 400 - 144 = 256, hence

ac =  \sqrt{256}256  = 16

now find ad² from δacd and δabd

δacd → ad² = 16² - (20 - x)² = 256 - 400 + 40x - x²

δabd → ad² = 12² - x² = 144 - x²

equate both equations for ad², hence

256 - 400 + 40x - x² = 144 - x²

-144 + 40x - x² = 144 - x² ( add x² to both sides )

- 144 + 40x = 144 ( add 144 to both sides )

40x = 288 ( divide both sides by 40 )

x = 7.2 → c