Question

a Rectanglular pen for a pet is 5 feet longer than it is wide. give possible values for the width W of the pen if its area must be between 176 and 760 square feet inclusively. The width of the pen ranges from the smaller value of the width--- feet, to the larger value of the width , ----feet , inclusively.

Answer 1

w(w+5) = 176
w^2 + 5 w - 176 = 0
(w -11)(w+16) = 0
w = 11

w^2 + 5 w = 760
w^2 + 5 w - 760 = 0
use quadratic equation
w = 25.18, 30.18 or 25.18 for width

so
smaller is 11 and bigger is 25.18