All of the following expressions are equal except_____. Help!!!!

Mathematics

1 answer:

9966 [12]3 years ago

7 0

The answer is the first one (a)

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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 betwee

gavmur [86]

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.

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