In the diagram below, the length of the legs AC and BC of right triangle ABC are 6 cm and 8 cm, respectively. Altitude
CD is drawn to the hypotenuse of AABC.
A
х
D
6 cm
С
8 cm
B
What is the length of AD to the nearest tenth of a
centimeter?
A 3.6
B 6.0
C 6.4
D 4.0

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So the first thing we do is to multiply the top equation by 3. the reason i want to do this is i notice there will be a 6y on both equations and can possibly add/subtract them. so we get 6y = -3x + 27. adding that and the second equation we get 6x = 27-15 which is 12. divide by 6 and we get 2. ∴ x = 2. substituting 2 into the first equation we get 2y = -2 + 9 which is 7. divide by 2 and we get 7/2. ∴ y = 7/2, x = 2.