Answer: The required distance between the top and bottom of the bridge is 76 feet.
Step-by-step explanation: Given that a new bridge structure requires triangles that are in a ratio of 1:1.
AC = 2x + 10 and EC = 4x − 18.
We are to find the distance between the top and bottom of the bridge, in feet.
Since the two triangles ACB and DCE are in the ratio 1 : 1, so their corresponding sides are also in the ratio 1 : 1.
The sides AC and EC are corresponding to each other, so we must have
[tex]AC:EC=1:1\\\\\Rightarrow \dfrac{AC}{EC}=\dfrac{1}{1}\\\\\Rightarrow AC=EC\\\\\Rightarrow 2x+10=4x-18\\\\\Rightarrow 4x-2x=10+18\\\\\Rightarrow 2x=28\\\\\Rightarrow x=\dfrac{28}{2}\\\\\Rightarrow x=14.[/tex]
Therefore, the distance between the top and bottom of the bridge is
[tex]EA\\\\=EC+AC\\\\=4x-18+2x+10\\\\=6x-8=6\times14-8\\\\=84-8\\\\=76~\textup{feet}.[/tex]
Thus, the required distance between the top and bottom of the bridge is 76 feet.
From the given ratios, it is found that the distance between the top and bottom of the bridge is of 76 feet.
The distance between the top and the bottom of the bridge is given by:
[tex]d = AC + EC[/tex]
The triangles are in a ratio of 1:1, thus:
[tex]AC = EC[/tex]
We have that:
[tex]AC = 2x + 10[/tex]
[tex]EC = 4x - 18[/tex]
Since they are equal:
[tex]AC = EC[/tex]
[tex]2x + 10 = 4x - 18[/tex]
[tex]2x = 28[/tex]
[tex]x = \frac{28}{2}[/tex]
[tex]x = 14[/tex]
Their measures are:
[tex]AC = 2x + 10 = 2(14) + 18 = 28 + 18 = 38[/tex]
[tex]EC = AC = 38[/tex]
Thus, the distance is of:
[tex]d = AC + EC = 38 + 38 = 76[/tex]
The distance is of 76 feet.
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