Question

What is the missing width of a rectangular prism with a length of 6 cm, a height of 4 cm, and a surface area of 188 cm2
?

Answer 1

To find the missing width of a rectangular prism, we can use the formula for the surface area of a rectangular prism:

\[
\text{Surface Area} = 2(lw + lh + wh)
\]

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

Given:
- Length \( l = 6 \, \text{cm} \)
- Height \( h = 4 \, \text{cm} \)
- Surface Area = 188 cm²

We can substitute the known values into the surface area formula:

\[
188 = 2(6w + 6 \cdot 4 + 4w)
\]

Calculating the constant parts first:

\[
188 = 2(6w + 24 + 4w)
\]

Combine the terms inside the parentheses:

\[
188 = 2(10w + 24)
\]

Now divide both sides by 2:

\[
94 = 10w + 24
\]

Next, subtract 24 from both sides:

\[
94 - 24 = 10w
\]
\[
70 = 10w
\]

Now, divide by 10:

\[
w = \frac{70}{10} = 7 \, \text{cm}
\]

So, the missing width of the rectangular prism is:

\[
\boxed{7 \, \text{cm}}
\]