Question

Please help with this question.

Answer 1

x = 4

Explanation:

Label the points from A-F. I attached an image of how I labeled the points.

Notice that there are similar triangles here:

• 
  `\triangle ABD \sim \triangle FED`
• 
  `\triangle ACD \sim \triangle AEF`

Set up proportions to find the values of x, y, and z.

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  `\displaystyle \text{Equation I: }(FD)/(AD) = (FE)/(AB)`
• 
  `\displaystyle \text{Equation II: } (A F)/(AD)=(EF)/(CD)`

Let's make this problem simpler by incorporating only 2 variables instead of 3. Let's say that the total distance between the two poles is distance d. Instead of z, let's call it d - y.

Substitute known values or variables into the proportions.

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  `\displaystyle \text{Equation I: } (d-y)/(d) = (x)/(6)`
• 
  `\displaystyle \text{Equation II: }(y)/(d)= (x)/(12)`

Cross-multiply and simplify Equation I.

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  `6(d-y)=dx`
• 
  `6d-6y=dx`

Cross-multiply and simplify Equation II.

• 
  `12y=dx`

We now have two equations that are equal to dx, so we can set them equal to each other.

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  `6d-6y=12y`

Add 6y to both sides of the equation.

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  `6d=18y`

Divide both sides of the equation by 6.

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  `d=3y`

We can substitute this value of d back into either Equation I or II. I am going to substitute d into Equation II.

• 
  `\displaystyle (y)/(3y) = (x)/(12)`

Cross-multiply and simplify the equation.

• 
  `12y=3xy`

Divide y from both sides of the equation.

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  `12=3x`

Divide both sides of the equation by 3.

• 
  `4=x`

The guylines from the top of one pole to the bottom of the other cross at the height of 4 ft off the ground.