Question

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
?(1 point)
cm

Answer 1

To find the missing width of a rectangular prism given its length, height, and surface area, 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,
- \( h \) is the height.

We are given:
- Length (\( l \)) = 6 cm,
- Height (\( h \)) = 4 cm,
- Surface Area = 188 cm².

We need to find the width (\( w \)).

Substituting the known values into the surface area formula:

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

This simplifies to:

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

Now combine like terms:

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

Now we divide both sides by 2:

\[
94 = 10w + 24
\]

Next, isolate the term with \( w \):

\[
94 - 24 = 10w
\]

\[
70 = 10w
\]

Now, divide both sides by 10:

\[
w = 7
\]

So, the missing width is \( \boxed{7} \) cm.