Question

select the correct answer a rectangular prism has a height of 15 centimeters and a width of 6 centimeters. the surface area of the prism is 684 square centimeters. what is the length of the prism? a. 24 cm b. 9 cm c. 12 cm d. 6 cm

Explanation:

Step1: Recall surface area formula for rectangular prism

The surface area \( S \) of a rectangular prism with length \( l \), width \( w \), and height \( h \) is given by the formula:
\( S = 2(lw + lh + wh) \)

We know \( h = 15 \, \text{cm} \), \( w = 6 \, \text{cm} \), and \( S = 684 \, \text{cm}^2 \). We need to solve for \( l \).

Step2: Substitute known values into the formula

Substitute \( h = 15 \), \( w = 6 \), and \( S = 684 \) into the formula:
\( 684 = 2(l \cdot 6 + l \cdot 15 + 6 \cdot 15) \)

Step3: Simplify the equation

First, divide both sides by 2:
\( \frac{684}{2} = l \cdot 6 + l \cdot 15 + 90 \)
\( 342 = 6l + 15l + 90 \)

Combine like terms (\( 6l + 15l = 21l \)):
\( 342 = 21l + 90 \)

Subtract 90 from both sides:
\( 342 - 90 = 21l \)
\( 252 = 21l \)

Step4: Solve for \( l \)

Divide both sides by 21:
\( l = \frac{252}{21} = 12 \)

Answer:

C. 12 cm