9514 1404 393
Answer:
1.5 cm
Step-by-step explanation:
All areas are in cm^2. For a width w, the border will have an area equal to the product of its centerline length and its width:
border area = 2((20-w) +(15-w))·w = w(70 -4w)
This area is 32% of the total cover area, so is ...
0.32(20)(15) = 96
Equating these expressions for the area gives ...
96 = 70w -4w^2
w^2 -17.5w = -24 . . . . . divide by -4
w^2 -17.5w +8.75^2 = -24 +8.75^2 . . . . . complete the square
(w -8.75)^2 = 52.5625 . . . . simplify
w -8.75 = ±√52.5625 = ±7.25
A border width only makes sense if it is between 0 and 7.5 cm, so the appropriate value for w is ...
w = 8.75 ± 7.25 . . . . . . . . . add 8.75
w = 8.75 -7.25 = 1.50 . . . . . the solution w=16 makes no sense
The border width is 1.5 cm.
