Britney takes a 9.4-inch by 3.1-inch rectangle of fabric and cuts from one corner of the piece of fabric to the diagonally opposite corner. Now Britney has two equally sized triangles of fabric. What is the perimeter of each triangle? If necessary, round to the nearest tenth.

To find the perimeter of each triangle, we first need to find the length of the diagonal (which is now the hypotenuse of each triangle) using the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as: a² + b² = c².

Here, the sides of the rectangle are 9.4 inches and 3.1 inches. So, we can calculate the diagonal as follows:

c² = a² + b² c² = (9.4)² + (3.1)² c² = 88.36 + 9.61 c² = 97.97

Taking the square root of both sides to solve for c (the diagonal), we get:

c = √97.97 c = 9.9 inches (rounded to the nearest tenth)

Now, the perimeter of each triangle is the sum of the lengths of all its sides. Since the triangles are right triangles and have one side that is the diagonal of the rectangle, the perimeter can be calculated as follows:

Perimeter = a + b + c Perimeter = 9.4 inches + 3.1 inches + 9.9 inches Perimeter = 22.4 inches

So, the perimeter of each triangle is 22.4 inches.