Question

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.

Explanation:

Step1: Set AC = EC (ratio 1:1)

Since the triangles are in a 1:1 ratio, their corresponding sides \( AC \) and \( EC \) are equal. So we set up the equation:
\( 2x + 10 = 4x - 18 \)

Step2: Solve for \( x \)

Subtract \( 2x \) from both sides:
\( 10 = 2x - 18 \)

Add 18 to both sides:
\( 28 = 2x \)

Divide by 2:
\( x = 14 \)

Step3: Find length of AC (or EC)

Substitute \( x = 14 \) into \( AC = 2x + 10 \):
\( AC = 2(14) + 10 = 28 + 10 = 38 \) ft

Step4: Find total distance (AC + EC)

Since \( AC = EC = 38 \) ft, the total distance is \( 38 + 38 = 76 \) ft.

Answer:

76 ft