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.

Distance between the top and bottom of the bridge is 76 feet

Solution:

The image of the question is attached below.

Ratio of the triangles is 1 : 1.

AC = 2x + 10 and EC = 4x − 18.

Since the two triangles ACB and DCE are in the ratio 1 : 1, so their corresponding sides are also in the ratio 1 : 1.

Therefore sides AC and EC are corresponding to each other.

AC : EC = 1 : 1

Subtract 10 from both sides of the equation.

Subtract 4x from both sides of the equation.

Divide by -2 on both sides, we get

⇒ x = 14

Distance between the top and bottom of the bridge is EA.

EA = AC + EC

     = 2x + 10 + 4x - 18

     = 6x - 8

     = 6(14) - 8

     = 84 - 8

EA = 76 feet

Distance between the top and bottom of the bridge is 76 feet.

solve systems of equations by graphing. a system of linear equations contains two or more equations e.g. y=0.5x+2 and y=x-2. the solution of such a system is the ordered pair that is a solution to both equations. to solve a system of linear equations graphically we graph both equations in the same coordinate system

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step-by-step explanation: