Question
find the missing side length of a square with a diagonal length of 46cm
Answers
Answered by
GPT-4o mini
To find the side length of a square given its diagonal length, you can use the formula relating the diagonal \( d \) to the side length \( s \) of a square:
\[
d = s\sqrt{2}
\]
You can rearrange this formula to solve for \( s \):
\[
s = \frac{d}{\sqrt{2}}
\]
Given that the diagonal \( d \) is 46 cm, you can substitute this value into the formula:
\[
s = \frac{46}{\sqrt{2}}
\]
To simplify this, multiply the numerator and denominator by \( \sqrt{2} \):
\[
s = \frac{46 \sqrt{2}}{2} = 23\sqrt{2} \, \text{cm}
\]
Now, you can calculate \( 23\sqrt{2} \) using the approximate value of \( \sqrt{2} \approx 1.414 \):
\[
s \approx 23 \times 1.414 \approx 32.66 \, \text{cm}
\]
Thus, the side length of the square is approximately \( 32.66 \, \text{cm} \).
\[
d = s\sqrt{2}
\]
You can rearrange this formula to solve for \( s \):
\[
s = \frac{d}{\sqrt{2}}
\]
Given that the diagonal \( d \) is 46 cm, you can substitute this value into the formula:
\[
s = \frac{46}{\sqrt{2}}
\]
To simplify this, multiply the numerator and denominator by \( \sqrt{2} \):
\[
s = \frac{46 \sqrt{2}}{2} = 23\sqrt{2} \, \text{cm}
\]
Now, you can calculate \( 23\sqrt{2} \) using the approximate value of \( \sqrt{2} \approx 1.414 \):
\[
s \approx 23 \times 1.414 \approx 32.66 \, \text{cm}
\]
Thus, the side length of the square is approximately \( 32.66 \, \text{cm} \).