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 = 4x − 3 and ec = 2x 6, find the distance between the top and bottom of the bridge, in feet. O 4.5 ft O 15 ft O 18 ft O 30 ft

Answer 1

To find the distance between the top and bottom of the bridge, we need to solve for the height of triangle ABC. Set up a proportion and solve for x. Substitute x back to find the distance between the top and bottom of the bridge is 30 ft.

Step-by-step explanation:

To find the distance between the top and bottom of the bridge, we need to solve for the height of triangle ABC. Since triangles ABC and EDC are similar and in a ratio of 1:1, we can set up a proportion to find the height of triangle ABC.

The proportion is:

(4x - 3)/3R = (2x + 6)/x

Cross-multiplying and solving for x gives:

2x^2 + 9x - 18 = 0

We can solve this quadratic equation and find the value of x. Once we have x, we can substitute it back into the expression for AC to find the distance between the top and bottom of the bridge.

The correct answer is 30 ft.