Question

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.

Answer 1

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

$\Rightarrow \frac{A C}{E C}=\frac{1}{1}$

$\Rightarrow A C=E C$

$\Rightarrow 2 x+10=4 x-18$

Subtract 10 from both sides of the equation.

$\Rightarrow 2 x=4 x-28$

Subtract 4x from both sides of the equation.

$\Rightarrow -2 x=-28$

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.