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.

The two triangles ACB and DCE are in the ratio 1 : 1, thus their corresponding sides are also in the ratio 1:1.. AC and EC are corresponding to each other

AC:EC= 1:1

We can also write it as:

AC/EC = 1/1

By cross multiplication we get

AC= EC

Now put the expressions of AC and EC.

2x+10 = 4x-18

Combine the like terms:

10+18=4x-2x

28=2x

Divide both sides by 2

2x/2 = 28/2

x= 14 feet

And now you can see in the attached picture distance of the top and bottom of the bridge is EA.

Therefore

EA = EC+AC

EC= 4x-18+2x+10

put the value x = 14

EC= 4(14)-18+2(14)+10

EC=56-18+28+10

EC= 76 feet

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

jajumonac jajumonac · Answer 2 · 2020-02-27T04:31:57+01:00

Answer:

76 feet.

Step-by-step explanation:

Givens

Triangles are in a ratio of 1:1. Basically, this means they are equal.
AC = 2x + 10 and EC = 4x - 18.

So, if those triangles are in a ratio of 1:1, then AC = EC, because they are corresponding sides.

[tex]AC = EC\\2x+10=4x-18[/tex]

Solving for [tex]x[/tex]

[tex]2x+10=4x-18\\10+18=4x-2x\\2x=28\\x=\frac{28}{2}\\ x=14[/tex]

Now, we know that the distance from the top to the botton can be expresed as

[tex]d=AC+EC[/tex]

Replacing the expressions of each side,

[tex]d=2x+10+4x-18\\d=6x-8\\d=6(14)-8=84-8\\d=76[/tex]

Therefore, the distance from top to bottom is 76 feet.