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A new bridge structure requires triangles that are in a ratio of 1:1. If AC = 5x − 5 and EC = 3x + 9, find the distance between the top and bottom of the bridge, in feet.

A. 7 ft
B. 30 ft
C. 60 ft
D. 90 ft

A new bridge structure requires triangles that are in a ratio of 11 If AC 5x 5 and EC 3x 9 find the distance between the top and bottom of the bridge in feet A class=

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znk

Answer:

C. 60 ft

Step-by-step explanation:

If triangles ABC and EDC are in a 1:1 relation, they are congruent, and  

    AC = EC

5x - 5 = 3x + 9

    5x = 3x + 14

    2x = 14

      x = 7

AC = 5x + 5 = 5(7) - 5 = 35 - 5 = 30 ft

EC = 3x + 9 = 3(7) + 9 = 21 + 9 = 30 ft

Distance between top and bottom of bridge = AC + EC = 30 + 30 = 60 ft

MrRoyal

Similar triangles have equal side lengths and measure of angles.

The distance between the top and bottom of the bridge, is 60 feet

The ratio of the triangle is 1 : 1.

So, we have:

[tex]\mathbf{AC = EC}[/tex]

This gives

[tex]\mathbf{5x - 5 = 3x + 9}[/tex]

Collect like terms

[tex]\mathbf{5x - 3x = 5 + 9}[/tex]

[tex]\mathbf{2x = 14}[/tex]

Divide both sides by 2

[tex]\mathbf{x = 7}[/tex]

So, the required distance is:

[tex]\mathbf{Distance = AC + EC}[/tex]

[tex]\mathbf{Distance = 5x - 5 + 3x + 9}[/tex]

[tex]\mathbf{Distance = 8x + 4}[/tex]

Substitute 7 for x

[tex]\mathbf{Distance = 8\times 7 + 4}[/tex]

[tex]\mathbf{Distance = 56 + 4}[/tex]

[tex]\mathbf{Distance = 60}[/tex]

Hence, the required distance is (c) 60 ft

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