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

Step-by-step explanation:

We have given that :

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....

Step-by-step explanation:

Givens

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

Solving for

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

Replacing the expressions of each side,

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

x = -2

y = 848

step-by-step explanation:

plug in the numbers