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.

Answer 1

The task is to solve for x by setting the lengths of sides AC and EC equal to each other for the two triangles that share vertex C, with the intent to maintain a 1:1 ratio. Solving the equation, we find x and then determine the length of side AC. A double-check is advised due to an unexpected negative result.

Step-by-step explanation:

The question involves finding the distance between the top and bottom of a bridge using the lengths of the sides of two triangles that share a common vertex. We are given that triangles ABC and EDC have a common vertex C, and that AC = 2x − 10 and EC = 4x + 18. Since the requirement is for the triangles to be in a ratio of 1:1, we set the side lengths equal to each other and solve for x:

• AC = EC
• 2x - 10 = 4x + 18
• 2x = -28 (by subtracting 4x and adding 10 to both sides)
• x = -14 (by dividing both sides by 2)

Once we have the value of x, we plug it into either expression for AC or EC to find the length of the side.

• AC = 2(-14) - 10
• AC = -28 - 10
• AC = -38 feet

However, the distance cannot be negative, so it's important to double-check the initial setup for any mistakes.