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A guy attached a wire, 24m long, to a vertical pole of height 18m and has a stake attached to the other end. The distance of the pole should the stake be driven so that the wire will be taut is ____.

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Detailed Solution

A guy attached a wire, 24m long, to a vertical pole of height 18m and has a stake attached to the other end. The distance of the pole should the stake be driven so that the wire will be taut is

6 \sqrt{7}

.
In right-angled triangles,

p^{2} + b^{2} = h^{2}

Sketching the diagram according to the question,
Question Image

Considering AB as the vertical pole, BC as the distance of the stake from the pole’s base and AC as the length of the wire we get,

\Rightarrow {AB}^{2} + {BC}^{2} = {AC}^{2}

\Rightarrow 18^{2} + {BC}^{2} = 24^{2}

\Rightarrow {BC}^{2} = 576 - 324

\Rightarrow BC = \sqrt{252}

\Rightarrow BC = 6 \sqrt{7}

m
Therefore, the required integer is

6 \sqrt{7}

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