Answer:
1. Anya's suggestion
2. Length is always positive
Step-by-step explanation:
Volume = length × width × height
1.
Volumes:
Anya's approach
1.5 is the height of the box
Since 2 squares are cut, the dimensions of the base reduce be 2×1.5 = 3
Volume = (11 - 3) × (8.5 - 3) × 1.5
= 55 in³
Terrence's approach
3 is the height of the box
Since 2 squares are cut, the dimensions of the base reduce be 2×3 = 6
Volume = (11 - 6) × (8.5 - 6) × 3
= 37.5 in³
2.
Dimensions of the base are:
(8.5-2x) × (11 - 2x)
Since length cannot be negative:
x > 0
8.5 - 2x > 0
2x < 8.5
x < 4.25
11 - 2x > 0
x < 5.5
The set of values of x which satisfies all is:
0 < x < 4.25