Question

a rectangular pen for a pet is7 feet longer than it is wide. Give possible values for the width W of the pen if its area must be between 228 and 800 square feet, inclusively.

Answer 1

l=7+w
area A=l*w=(7+w)w =w^2 +7w>228 but w^2 +7w<800
w^2 +7w -228>0
-7+/-radical(49+912) -7+/- radical961 -7+/-31
w_1,_2=-------------------- = ---------------- =--------- = -19 and 12
2 2 2
- so when the width is grater than 12 feet the area is grater than 228 square feet

w^2 +7w<800
w^2 +7w -800 <0
-7+/- radical(49+3200) -7+/- radical3249 -7+/-57
w_1,_2 =---------------------- = ----------------- = ---------- = -32 and
2 2 2
25

- so hence for this area between 228 and 800 square feet the possible values of width W is from 12 feet till 25 feet