The surface area \( SA \) of a square pyramid can be calculated using the formula:
\[ SA = b^2 + 2bs \]
where:
- \( b \) is the length of the base,
- \( s \) is the slant height.
Given:
- \( b = 40 \) inches,
- \( SA = 2800 \) square inches.
First, we can calculate \( b^2 \):
\[ b^2 = 40^2 = 1600 \text{ square inches} \]
Now we can substitute \( b \) and \( SA \) into the surface area formula:
\[ 2800 = 1600 + 2(40)s \]
Simplifying this, we have:
\[ 2800 = 1600 + 80s \]
Now, subtract \( 1600 \) from both sides:
\[ 2800 - 1600 = 80s \] \[ 1200 = 80s \]
Next, divide both sides by \( 80 \) to solve for \( s \):
\[ s = \frac{1200}{80} = 15 \text{ inches} \]
Thus, the slant height \( s \) is:
\[ \boxed{15} \text{ inches} \]
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