Atriangular paddock has a road ab forming its hypotenuse. ab is 3 km long. the fences ac and cb are at right angles. if bc is 400 m longer than ac, find the area of the paddock in hectares.

Since the paddock assumes a rectangular shape the area is 1/2 * b * h. From Pythagorean AB^2 = BC^2 + AC^2 (3)^2 = (x + 0.4)^2 + x^2 9 = x^2 + 0.8x + 0.16 + x^2 So 2x^2 + 0.8x + 0.16 - 9 = 0 2x^2 +0.8x- 8.84 = 0 Using the quadratic formula The solutions are 1.911 and -2.31 The area therefore is area=1/2 * b * h =1.91*2.31/2 = 2.21km² 1hectare = 0.01km² 2.21km^2 = 221ha

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