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
[tex]$\Rightarrow \frac{A C}{E C}=\frac{1}{1}[/tex]
[tex]\Rightarrow A C=E C[/tex]
[tex]\Rightarrow 2 x+10=4 x-18[/tex]
Subtract 10 from both sides of the equation.
[tex]\Rightarrow 2 x=4 x-28[/tex]
Subtract 4x from both sides of the equation.
[tex]\Rightarrow -2 x=-28[/tex]
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.
