To find the relationship between \( b \) and \( h \), we start with the equation given:
\[ b = \frac{a}{h} \]
We also know that \( b = 8 \) when \( h = 5 \). We can use this information to find \( a \):
\[ 8 = \frac{a}{5} \]
Multiplying both sides by 5 gives:
\[ a = 8 \times 5 = 40 \]
Now we can rewrite our original equation using the value of \( a \):
\[ b = \frac{40}{h} \]
Next, we can find \( b \) when \( h = 4 \):
\[ b = \frac{40}{4} = 10 \]
Now, to find \( h \) when \( b = \frac{1}{4} \):
\[ \frac{1}{4} = \frac{40}{h} \]
Cross-multiplying gives:
\[ 1 \cdot h = 4 \cdot 40 \]
Thus:
\[ h = 160 \]
To summarize:
- When \( h = 4 \), \( b = 10 \).
- When \( b = \frac{1}{4} \), \( h = 160 \).