Question

A rectangular prism has a surface area of 160 square centimeters. The length of the prism is 10 centimeters and its height is 5 centimeters. Find the width of the prism.
A. 2 centimeters
B. 4 centimeters
C.
6 centimeters
D. 8 centimeters

Answer 1

To find the width of the rectangular prism, we can use the formula for the surface area \( S \) of a rectangular prism:

\[
S = 2(lw + lh + wh)
\]

where:
- \( l \) is the length,
- \( w \) is the width, and
- \( h \) is the height.

Given the surface area \( S = 160 \) square centimeters, length \( l = 10 \) centimeters, and height \( h = 5 \) centimeters, we can substitute these values into the formula:

\[
160 = 2(10w + 10 \cdot 5 + 5w)
\]

Calculating \( 10 \cdot 5 \):

\[
10 \cdot 5 = 50
\]

Now substituting this back into the equation:

\[
160 = 2(10w + 50 + 5w)
\]

Simplifying further:

\[
160 = 2(15w + 50)
\]

Dividing both sides by 2:

\[
80 = 15w + 50
\]

Subtracting 50 from both sides:

\[
80 - 50 = 15w
\]

\[
30 = 15w
\]

Dividing both sides by 15 to solve for \( w \):

\[
w = \frac{30}{15} = 2
\]

Thus, the width of the prism is \( 2 \) centimeters.

Therefore, the answer is:
**A. 2 centimeters**