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 the length, height, and surface area, you 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:
- Length \( l = 6 \) cm,
- Height \( h = 4 \) cm,
- Surface area \( S = 188 \) cm².

Inserting the known values into the surface area formula gives:

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

This simplifies to:

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

Combining like terms inside the parentheses:

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

Dividing both sides by 2:

\[
94 = 10w + 24
\]

Now, isolating \( w \):

\[
94 - 24 = 10w
\]

Calculating the left side:

\[
70 = 10w
\]

Finally, dividing by 10:

\[
w = 7 \, \text{cm}
\]

So, the missing width is **7 cm**.