Question

A new bridge structure requires triangles that are in a ratio of 1:1.If AC = 2x + 6 and EC = 5x − 9, find the distance between the top and bottom of the bridge, in feet.

Answer 1

Solution

Step 1

From the figure, AC = EC

$2x\text{ + 6 = 5x - 9}$

Step 2

Solve for x.

$\begin{gathered} 2x\text{ + 6 = 5x - 9} \\ 6\text{ + 9 = 5x - 2x} \\ 15\text{ = 3x} \\ \text{x = }\frac{15}{3} \\ x\text{ = 5} \end{gathered}$

Step 3

The distance between the top and bottom of the bridge

$\begin{gathered} =\text{ AC + EC} \\ =\text{ 2x + 6 + 5x - 9} \\ =\text{ 7x - 3} \\ =\text{ 7}\times5\text{ - 3} \\ =\text{ 35 - 3} \\ =\text{ 32} \end{gathered}$

Final answer

32 feet