To find the length of each side of the square given that its diagonal (which is the hypotenuse of the resulting right triangles) is 30 inches long, we can use the relationship between the side length of the square and its diagonal.
For a square with side length \( s \), the length of the diagonal \( d \) can be found using the Pythagorean theorem:
\[ d = s\sqrt{2} \]
Given the diagonal \( d \) is 30 inches, we can set up the equation:
\[ 30 = s\sqrt{2} \]
To solve for \( s \), we divide both sides by \( \sqrt{2} \):
\[ s = \frac{30}{\sqrt{2}} \]
To simplify, we can multiply the numerator and the denominator by \( \sqrt{2} \):
\[ s = \frac{30 \sqrt{2}}{2} \]
\[ s = 15\sqrt{2} \]
We can approximate \( \sqrt{2} \) as 1.414:
\[ s \approx 15 \times 1.414 \]
\[ s \approx 21.21 \]
Therefore, the length of each side of the square is approximately \( 21.21 \) inches.
The correct answer is:
\[ 21.21 \text{ inches} \]
A square is cut on the diagonal to form 2 right triangles. The hypotenuse of the resulting triangles is 30 inches long.
What is the length of each side of the square?
3.87 inches
5.48 inches
15 inches
21.21 inches
1 answer
1 answer