Question

Wut is da 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:

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

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

Given:
- \( \text{Surface Area} = 188 \, \text{cm}^2 \)
- \( l = 6 \, \text{cm} \)
- \( h = 4 \, \text{cm} \)

We need to find \( w \).

Substituting the known values into the surface area formula:

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

Calculating \( 2(6)(4) \):

\[
2(6)(4) = 48
\]

So, we can substitute that back into the equation:

\[
188 = 12w + 48 + 8w
\]

Now, combine like terms:

\[
188 = 20w + 48
\]

Next, subtract 48 from both sides to isolate the term with \( w \):

\[
188 - 48 = 20w
\]

\[
140 = 20w
\]

Now, divide both sides by 20:

\[
w = \frac{140}{20} = 7
\]

Therefore, the missing width \( w \) is:

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