A rectangular field is enclosed on 3 sides by a fence, while the 4th side is a stream. The fence opposite the stream is 150 m longer than the other sides. If the area of the field is 70,000 m2, find its dimensions.

Question

campbell_st · Answer

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let the width of the field be x then the length is x + 150

Area = Length x width

so 

$$70000 = x(x + 150) .... or....  x^2 + 150x - 70000 = 0$$

solve the quadratic to find the dimensions. 

factorising 

(x + 350)(x - 200) = 0

then x = -350 or 200

only consider the positive measurement 

so the width is 200 metres and the length is 350 metres