Joey has a square piece of paper with edges that are 8 inches long.  He cuts the paper along a diagonal to make two congruent triangles.  Which measurement is closest, in inches, to the length of the hypotenuse of each triangle?

Joey cuts a square piece of paper with 8-inch edges along its diagonal, creating two congruent right triangles. The length of the hypotenuse of these triangles is the diagonal of the square.

### Step 1: Recognize the situation
In this case, each triangle is a right triangle with two legs equal to the sides of the square, i.e., 8 inches. The hypotenuse of these triangles is the diagonal of the square.

### Step 2: Apply the Pythagorean theorem
Since the legs of the triangles are both 8 inches, we use the Pythagorean theorem to find the hypotenuse \( c \):
\[
c = \sqrt{a^2 + b^2}
\]
Here, \( a = 8 \) inches and \( b = 8 \) inches:
\[
c = \sqrt{8^2 + 8^2} = \sqrt{64 + 64} = \sqrt{128}
\]
\[
c \approx \sqrt{128} \approx 11.31 \, \text{inches}
\]

### Conclusion
The length of the hypotenuse of each triangle is approximately **11.31 inches**.

Would you like more details or have any questions?

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Here are 8 related questions:
1. What is the area of each of the congruent triangles after the cut?
2. How do you find the perimeter of one of the triangles?
3. How does the diagonal of a square relate to its side length?
4. How would the diagonal change if the square’s side was doubled?
5. Can the hypotenuse be found using trigonometric functions for other triangle types?
6. What happens to the triangle’s hypotenuse if the square is cut differently?
7. How do the angles in these triangles relate to the side lengths?
8. How can you use the Pythagorean theorem in 3D problems?

Tip: The diagonal of a square can be calculated using the formula \( \text{diagonal} = s\sqrt{2} \), where \( s \) is the side length.

Discover how to calculate the length of the hypotenuse of two congruent triangles formed by cutting an 8-inch square paper along its diagonal. Use the Pythagorean theorem to find the solution. Suitable for Grades 7-9.

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