A grade 10 quadratic word problem.?

A chemical planet is rectangular and has a length of 100 m and a width of 60m. A safety zone of uniform width surrounds the plant. If the area of the safety zone equals the area pf the plant, what is the width of the safety zone?

please show your work

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  • 1 decade ago
    Favorite Answer

    it's about 15.7

    b/c

    (100+2x)(60+2x)-6000=6000

    4x^2+320x-6000=0

    x=15.678

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  • 1 decade ago

    Call the width W. The plant forms an 100x60 rectangle, surrounded by an outer rectangle formed for the safety zone of the plant. The length of this outer rectangle is 100+W and the width is 60+W.

    The area of the safety zone itself is the difference between the areas of the two rectangles (a diagram would help here).

    So the equation is: (W+60)*(W+100) - 100*60 = 100*60

    w^2 + 160w + 6000 - 6000 = 6000

    w^2 + 160w - 6000 = 0

    Use the quadratic formula to solve

    There are 2 answers: w=31.355 m , w=-191.36m

    Therefore the width of the safety zone is 31.355 m.

    10pts please =)

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