To find Miranda's height based on the lengths of their shadows, we can set up a proportion.
Emily's height is 5 feet and her shadow is 28 inches. We convert Emily's height to inches for consistency:
\[ 5 \text{ feet} = 5 \times 12 = 60 \text{ inches} \]
Now we know:
- Emily's height = 60 inches
- Emily's shadow = 28 inches
Let Miranda's height be \( h \) inches. Her shadow is 29.4 inches. The ratio of height to shadow length for both Emily and Miranda can be set equal:
\[ \frac{\text{Emily's height}}{\text{Emily's shadow}} = \frac{\text{Miranda's height}}{\text{Miranda's shadow}} \]
Substituting the values into the equation gives:
\[ \frac{60}{28} = \frac{h}{29.4} \]
We can cross-multiply to solve for \( h \):
\[ 60 \cdot 29.4 = 28 \cdot h \]
Calculating \( 60 \cdot 29.4 \):
\[ 60 \cdot 29.4 = 1764 \]
Now, we can set up the equation:
\[ 1764 = 28h \]
Now, divide both sides by 28 to solve for \( h \):
\[ h = \frac{1764}{28} = 63 \]
Now, converting this back to feet:
\[ h = \frac{63}{12} \text{ feet} = 5.25 \text{ feet} \]
Thus, approximately, Miranda is 5 1/4 feet tall. Therefore, the correct answer is:
5 1/4 feet.
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