Question

15 if a rectangular prism with a length of 12 feet and a width of 9 feet has a surface area of 930 square feet, find its height.

Explanation:

Step1: Recall surface area formula

The surface area $S$ of a rectangular prism is given by:
$$S = 2(lw + lh + wh)$$
where $l=12$ ft, $w=9$ ft, $S=930$ sq ft, and $h$ is the unknown height.

Step2: Substitute known values

$$930 = 2((12 \times 9) + 12h + 9h)$$

Step3: Simplify inside the parentheses

Calculate $12 \times 9 = 108$, and combine like terms:
$$930 = 2(108 + 21h)$$

Step4: Divide both sides by 2

$$\frac{930}{2} = 108 + 21h$$
$$465 = 108 + 21h$$

Step5: Isolate the term with $h$

Subtract 108 from both sides:
$$465 - 108 = 21h$$
$$357 = 21h$$

Step6: Solve for $h$

Divide both sides by 21:
$$h = \frac{357}{21}$$

Answer:

17 feet