Question

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
4.5 ft
15 ft
18 ft
30 ft

Explanation:

Step1: Set AC equal to EC (ratio 1:1)

Since the triangles are in a ratio of 1:1, their corresponding sides \( AC \) and \( EC \) are equal. So we set up the equation:
\( 4x - 3 = 2x + 6 \)

Step2: Solve for x

Subtract \( 2x \) from both sides:
\( 4x - 2x - 3 = 6 \)
\( 2x - 3 = 6 \)

Add 3 to both sides:
\( 2x = 6 + 3 \)
\( 2x = 9 \)

Divide both sides by 2:
\( x = \frac{9}{2} = 4.5 \)

Step3: Find length of AC (or EC)

Substitute \( x = 4.5 \) into \( AC = 4x - 3 \):
\( AC = 4(4.5) - 3 = 18 - 3 = 15 \)

Step4: Find total distance (AC + EC)

Since \( AC = EC = 15 \), the total distance between top and bottom is \( AC + EC = 15 + 15 = 30 \)

Answer:

30 ft