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.

Answer 1

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

$AC:EC=1:1\\\\\Rightarrow \dfrac{AC}{EC}=\dfrac{1}{1}\\\\\Rightarrow AC=EC\\\\\Rightarrow 2x+10=4x-18\\\\\Rightarrow 4x-2x=10+18\\\\\Rightarrow 2x=28\\\\\Rightarrow x=\dfrac{28}{2}\\\\\Rightarrow x=14.$

Therefore, the distance between the top and bottom of the bridge is

$EA\\\\=EC+AC\\\\=4x-18+2x+10\\\\=6x-8=6\times14-8\\\\=84-8\\\\=76~\textup{feet}.$

Thus, the required distance between the top and bottom of the bridge is 76 feet.