Question

What is the length of AC?

Answer 1

Explanation:

These triangles are similar. That means that the corresponding side lengths exist in proportion to one another. Namely,

`(DE)/(BA)=(CE)/(CA)`

Filling in those values gives us

`(9)/(81)=(x)/(140-x)` and cross multiply to solve:

9(140 - x) = 81x and

1260 - 9x = 81x and

1260 = 90x so

x = 14

That means that side length AC is 140 - 14 which is 126. Choice B.

Answer 2

126

Option B is the right option.

Solution,

`(140 - x)/(x) = (81)/(9) \\ or \: (140 - x)/(x) = 9 \\ or \: 140 - x = 9x \\ or \: - x - 9x = 140 \\ or \: - 10x = 140 \\ or \: x = ( - 140)/( - 10) \\ x = 14 \\ again \\ ac = 140 - 14 \\ \: \: \: \: \: \: \: = 126`

hope this helps...

Good luck on your assignment..