The surface area of a rectangular prism is 220 cm². Two of the dimensions are 5 cm and 10 cm. Find the measure of the other dimension.

Steps to Solve

1. Identify the surface area formula for a rectangular prism

The formula for the surface area $S$ of a rectangular prism with dimensions length $l$, width $w$, and height $h$ is given by:

$$ S = 2(lw + lh + wh) $$

2. Substitute known values into the formula

We know:

• Surface area ($S$) = 220 cm²
• Length ($l$) = 5 cm
• Width ($w$) = 10 cm

Substituting these values into the surface area formula gives:

$$ 220 = 2(5 \times 10 + 5 \times h + 10 \times h) $$

3. Simplify the equation

Calculating the area term yields:

$$ 220 = 2(50 + 5h + 10h) $$

So, we simplify it further:

$$ 220 = 2(50 + 15h) $$

4. Remove the factor of 2

Divide both sides by 2 to simplify the equation:

$$ 110 = 50 + 15h $$

5. Isolate $h$

To find $h$, subtract 50 from both sides:

$$ 110 - 50 = 15h $$

This results in:

$$ 60 = 15h $$

6. Solve for $h$

Now, divide by 15:

$$ h = \frac{60}{15} = 4 $$