To find the length of one side of a square frame given that its area is 55 square inches, we can use the formula for the area of a square:
\[ \text{Area} = \text{side}^2 \]
Let \(s\) represent the length of one side of the square. Therefore, we can set up the equation:
\[ s^2 = 55 \]
To find \(s\), we take the square root of both sides:
\[ s = \sqrt{55} \]
Now let's calculate the square root of 55.
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Using a calculator:
\[ s \approx 7.416198 \]
Now we can round this value as requested:
Part a: To the nearest whole inch
Rounding \(7.416198\) to the nearest whole inch gives us:
- The integer part is 7. Since .416 is less than .5, we round down.
Thus, the length of one side of the frame to the nearest whole inch is:
\[ \text{Length} \approx 7 \text{ in} \]
Part b: To the nearest tenth of an inch
Rounding \(7.416198\) to the nearest tenth gives us:
- The tenths place is 4, and the digit after it is 1 (which is less than 5), so we round down.
Thus, the length of one side of the frame to the nearest tenth of an inch is:
\[ \text{Length} \approx 7.4 \text{ in} \]
Summary of Results:
a. The length of one side of the frame to the nearest whole inch is 7 in.
b. The length of one side of the frame to the nearest tenth of an inch is 7.4 in.