QUESTION IMAGE
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. 9 cm
b. 24 cm
c. 12 cm
d. 8 cm
Step1: Recall surface area formula
The surface area \( S \) of a rectangular prism is given by:
$$S = 2(lw + lh + wh)$$
where \( l \) = length, \( w \) = width, \( h \) = height.
Step2: Plug in known values
We know \( S = 584 \, \text{cm}^2 \), \( w = 6 \, \text{cm} \), \( h = 15 \, \text{cm} \):
$$584 = 2(l \times 6 + l \times 15 + 6 \times 15)$$
Step3: Simplify the equation
First calculate \( 6 \times 15 = 90 \), then combine like terms inside the parentheses:
$$584 = 2(6l + 15l + 90)$$
$$584 = 2(21l + 90)$$
Divide both sides by 2:
$$292 = 21l + 90$$
Step4: Solve for \( l \)
Subtract 90 from both sides:
$$292 - 90 = 21l$$
$$202 = 21l$$
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Step1: Recall surface area formula
The surface area \( S \) of a rectangular prism is given by:
$$S = 2(lw + lh + wh)$$
where \( l \) = length, \( w \) = width, \( h \) = height.
Step2: Plug in known values
We know \( S = 584 \, \text{cm}^2 \), \( w = 6 \, \text{cm} \), \( h = 15 \, \text{cm} \):
$$584 = 2(l \times 6 + l \times 15 + 6 \times 15)$$
Step3: Simplify the equation
First calculate \( 6 \times 15 = 90 \), then combine like terms inside the parentheses:
$$584 = 2(6l + 15l + 90)$$
$$584 = 2(21l + 90)$$
Divide both sides by 2:
$$292 = 21l + 90$$
Step4: Solve for \( l \)
Subtract 90 from both sides:
$$292 - 90 = 21l$$
$$202 = 21l$$
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