Question

A company is designing a box in the shape of a rectangular prism. The surface area of the box can be represented as
2
(
x
+
2
)
2
+
4
(
x
+
2
)
(
x
+
4
)
for some positive number
x
.

Based on this expression, select three true statements regarding the company's box design.

The area of each square side of the box is
2
(
x
+
2
)
2
.


The length of each square side of the box is
(
x
+
2
)
2
.


There are exactly two identical square sides to the box.


There are exactly four identical non-square sides to the box.


The area of each non-square side of the box is
(
x
+
2
)
(
x
+
4
)
.

Answer 1

True statements:
- There are exactly two identical square sides to the box.
- There are exactly four identical non-square sides to the box.
- The area of each non-square side of the box is (x+2)(x+4).

Reason: 2(x+2)^2 indicates two faces each of area (x+2)^2 (so each square side has side length x+2), and 4(x+2)(x+4) indicates four faces each of area (x+2)(x+4). The first two given statements are false (2(x+2)^2 is the total area of the two square faces, and the side length is x+2, not (x+2)^2).