Question

A company is considering two different packages for a new product. The diagram shows the dimensions for the rectangular prism and the cylinder in inches.



image



The height of both packages is the same. The area of the base for the rectangular prism is
2
x
2
.

The surface area of the rectangular prism container can be represented by the expression
2
(
2
x
2
)
+
2
(
2
x
)
(
20
)
+
2
(
x
)
(
20
)
.



Which TWO expressions are equivalent that represent the surface area of the right prism?



A.
4
x
(
x
+
30
)

B.
4
x
(
4
x
+
30
)

C.
4
x
(
x
+
120
)

D.
4
x
2
+
40
x
(
2
)

E.
4
x
2
+
40
x
(
2
+
1
)

Answer 1

Compute the given expression:
2(2x^2) + 2(2x)(20) + 2(x)(20)
= 4x^2 + 80x + 40x
= 4x^2 + 120x
= 4x(x + 30).

This matches choice A (4x(x + 30)). It also matches E, since 4x^2 + 40x(2+1) = 4x^2 + 120x.

Answer: A and E.