SOLUTION: A wire is stretched from the ground to the top of an antenna tower. The wire is 20ft long. The height of the tower is 4ft greater than the distance d from the towers base to the e

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Question 519871: A wire is stretched from the ground to the top of an antenna tower. The wire is 20ft long. The height of the tower is 4ft greater than the distance d from the towers base to the end of the wire. Find the distance d and the height of the tower.
The section of the book I'm in is polynomial equations and functions. I came with
1/2d(d+4)=20 then I did 2/1 x 1/2d(d+4)=20 x 1/2 =d^2+4d=40=d^2+4d-40=0
I then tried to factor but it comes out prime for me but the answer in the back of the book is 12 and 16 ???
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
A wire is stretched from the ground to the top of an antenna tower. The wire is 20ft long. The height of the tower is 4ft greater than the distance d from the towers base to the end of the wire. Find the distance d and the height of the tower.
the answer in the back of the book is 12 and 16 ???
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Draw the picture.
You have a right triangle with hypotenuse = 20 ft.
Base of the triangle is "x":
Height of the triangle is "x+4".
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Equation:
x^2 + (x+4)^2 = 20^2
x^2 + x^2 + 8x + 16 = 400
2x^2 + 8x - 384 = 0
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x^2 + 4x - 192 = 0
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(x+16)(x-12) = 0
Positive solution:
x = 12 (distance to the pole.
x+4 = 16 (height of the pole)
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Cheers,
Stan H.
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