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.
2 centimeters
4 centimeters
6 centimeters
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, which is given by:

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

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

Given that the surface area \( S = 160 \) cm², the length \( l = 10 \) cm, and the height \( h = 5 \) cm, we can substitute these values into the formula:

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

First, simplify the expression inside the parentheses:

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

Combine the terms:

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

Now divide both sides by 2:

\[
80 = 15w + 50
\]

Next, isolate \( w \) by subtracting 50 from both sides:

\[
80 - 50 = 15w
\]
\[
30 = 15w
\]

Now, divide by 15:

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

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