SOLUTION: a rectangle field measure 24ft by 100ft part of the lawn is torn up to install a walk to uniform width around it the area of the new field is one half the area how wide is the walk

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Question 762311: a rectangle field measure 24ft by 100ft part of the lawn is torn up to install a walk to uniform width around it the area of the new field is one half the area how wide is the walk ? could someone help me please
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Area before new walkway is 24*100 sq. ft. This will also be the combined areas of the new, remaining field and the new walkway.
New field will be area of %2824-2w%29%28100-2w%29 sq. ft. using w as the width of the walkway.

New field is half the area of the original field:
highlight%28%281%2F2%29%282400%29=%2824-2w%29%28100-2w%29%29
Find w.

1200=4%2812-w%29%2850-w%29
300=%2812-w%29%2850-w%29
.
w%5E2-62w%2B300=0
w=%2862%2B2%2Asqrt%28661%29%29%2F2
highlight%28w=31%2Bsqrt%28661%29%29