A rectangular pen for a pet is 6 feet longer than it is wide. Give possible values for the width W of the pen if its area must be between 187 and 775 square feet, inclusively.

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anonymous · Answer

ok,so let the width be x. now the length is (x+6). the area is therefore x(x+6)= x^2 +6x. now since this areahas to be between 187 and 775, we have an inequality as follows: 187< x^2 + 6x <775. Now we look at each side of the inequality as separate equations. so we have 187=x^2 + 6x and x^2 + 6x=775. the first equation can be written as x^2 + 6x -187=0 and when solving for x we get x=-17 and x=11. now we know the width cannot be negative,so our lower bound of our inequality is 11. do the same for equation 2 and you will get x=-31 and x=25. agen we cannot get a negative number for width so our upper bound is 25. therefore the range on the width is: 11<x<25