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A fox and an eagle lived at the top of a cliff of height 6m whose base is at a distance of 10m from a point A on the ground.the fox descend the cliff and

went stright to the point A. the eagle flew vertically up to a height x metres and then flew in a straight line to a point A, the distance travelled by each being the same. find x.



It is apparent that fox travelled 16 m which is same as distance travelled by eagle. Now the eagle ascends to a height x m and reaches A. Distance travelled by eagle is √(10²+(6+x)²) + x. This is equal to 16 m. Then 100 + 36 + 12x + x² = 256 + x² - 32x⇒ = 0. Then x=120/44 = 30/11m.
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