Question

Triangles ABC and EDC are outlined on a bridge. The triangles share vertex C and angles D and B are right angles.

A new bridge structure requires triangles that are in a ratio of 1:1. If AC = 2x + 10 and EC = 4x − 18, find the distance between the top and bottom of the bridge, in feet.

14 ft
38 ft
76 ft
150 ft

Answer 1

[AI-generated answer — Bot GPT 3.5]

Let's first find the value of x by setting AC = EC:

2x + 10 = 4x - 18
28 = 2x
x = 14

Now, we can find the length of AC:
AC = 2(14) + 10 = 38 feet

To find the distance between the top and bottom of the bridge, we need to find the total height which is equal to AB + ED:

AB = AC/2 = 38/2 = 19 feet

ED = EC/2 = (4(14) - 18)/2 = 26 feet

Therefore, the distance between the top and bottom of the bridge is:
19 + 26 = 45 feet

So, the closest answer choice is 38 ft.