Question

the surface area of this rectangular prism is 860 square yards. what is the value of p? 16.7 yd, 8 yd, p. p = \boxed{} yards

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 \( S = 2(lw + lh + wh) \). Here, \( l = 16.7 \) yd, \( w = p \) yd, \( h = 8 \) yd, and \( S = 860 \) square yards. So we substitute these values into the formula:
\( 860 = 2(16.7p + 16.7\times8 + 8p) \)

Step2: Simplify the equation

First, divide both sides by 2:
\( \frac{860}{2}=16.7p + 133.6 + 8p \)
\( 430 = 24.7p + 133.6 \)

Step3: Solve for \( p \)

Subtract 133.6 from both sides:
\( 430 - 133.6 = 24.7p \)
\( 296.4 = 24.7p \)
Then divide both sides by 24.7:
\( p=\frac{296.4}{24.7} \)
\( p = 12 \)

Answer:

12