A wire is attached to the top of a pole. The wire is 7 ft longer than the pole, and the distance from the wire to the bottom of the pole is 7 ft less than the height of the pole. Find the length of the wire and the height of the pole. The length of the wire is ? ft, and the height of the pole is ? ft.

Question

A wire is attached to the top of a pole. The wire is 7 ft longer than the pole, and the distance from the wire to the bottom of the pole is 7 ft less than the height of the pole. Find the length of the wire and the height of the pole.    The length of the wire is ? ft, and the height of the pole is ? ft.

izboknil3 · Accepted Answer

Step 1 Let x be the height of the pole so that x+7 is the lenght of the wire and the distance from the wire to the bottom of the pole is x - 7, all in ft. Label the right triangle as shown:  Step 2 Using Pythagorean Theorem, we solve for x: x2+(x−7)2=(x+7)2 x2+x2−14x+49=x2+14x+49 2x2−14x+49=x2+14x+49 x2−28x=0 Factor: x(x-28)=0 By zero product property, x=0,28 The height of the pole cannot be 0 so we tale x = 28 as the solution. So, the lenght of the wire is 28 + 7 = 35 ft and the height of the pole is 28 ft. Result: The lenght of the wire is 35 ft, and the height of the pole is 28 ft.

Jeffrey Jordon · Accepted Answer

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A wire is attached to the top of a pole. The wire is 7 ft longer than the pole, and the distance from the wire to the bottom of the pole is 7 ft less

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