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प्रश्न
A pole has to be erected at a point on the boundary of a circular ground of diameter 20 m in such a way that the difference of its distances from two diametrically opposite fixed gates P and Q on the boundary is 4 m. Is it possible to do so? If answer is yes at what distance from the two gates should the pole be erected?
उत्तर
Let “R” be the required location of the pole
Let the distance from the gate P is “x” m : PR = “x” m
The distance from the gate Q is (x + 4)m
∴ QR = (x + 4)m
In the right ∆PQR,
PR2 + QR2 = PQ2 (By Pythagoras theorem)
x2 + (x + 4)2 = 202
x2 + x2 + 16 + 8x = 400
2x2 + 8x – 384 = 0
x2 + 4x – 192 = 0 ...(divided by 2)
(x + 16) (x – 12) = 0
x + 16 = 0 or x – 12 = 0 ...[negative value is not considered]
x = – 16 or x = 12
Yes it is possible to erect
The distance from the two gates are 12 m and 16 m
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