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

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,
- \( h \) is the height.

Given:
- \( S = 160 \) cm²,
- \( l = 10 \) cm,
- \( h = 5 \) cm.

We can substitute these values into the surface area formula:

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

Simplifying the equation:

1. Calculate \( 10 \cdot 5 \):

\[
10 \cdot 5 = 50
\]

2. Substitute it back into the equation:

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

3. Combine like terms inside the parentheses:

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

4. Now, divide both sides by 2:

\[
80 = 15w + 50
\]

5. Subtract 50 from both sides:

\[
30 = 15w
\]

6. Divide by 15:

\[
w = 2
\]

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