Certainly! Let's walk through the solution step-by-step:
### Step 1: Understand the Problem
Naomi has a rectangle with dimensions 52 inches by 39 inches. She cuts the rectangle diagonally from one corner to the opposite corner, forming two right-angled triangles of fabric. We need to determine the perimeter of each of these triangles.
### Step 2: Determine the Hypotenuse
In a right-angled triangle, the hypotenuse can be found using the Pythagorean theorem. For a right-angled triangle with legs [tex]\(a\)[/tex] and [tex]\(b\)[/tex], the hypotenuse [tex]\(c\)[/tex] can be calculated as:
[tex]\[ c = \sqrt{a^2 + b^2} \][/tex]
Here, the legs of the triangle are 52 inches and 39 inches.
### Step 3: Calculate the Hypotenuse
Using the given dimensions:
[tex]\[ a = 52 \][/tex]
[tex]\[ b = 39 \][/tex]
The hypotenuse [tex]\(c\)[/tex] is:
[tex]\[ c = \sqrt{52^2 + 39^2} \][/tex]
[tex]\[ c = \sqrt{2704 + 1521} \][/tex]
[tex]\[ c = \sqrt{4225} \][/tex]
[tex]\[ c = 65.0 \][/tex]
### Step 4: Calculate the Perimeter of One Triangle
The perimeter of a triangle is the sum of the lengths of its three sides. For each of the right-angled triangles obtained by cutting the rectangle diagonally, the sides are 52 inches, 39 inches, and the hypotenuse 65 inches.
Thus, the perimeter [tex]\(P\)[/tex] of one triangle is:
[tex]\[ P = 52 + 39 + 65 \][/tex]
[tex]\[ P = 156.0 \][/tex]
### Conclusion
The hypotenuse of each triangle is 65 inches, and the perimeter of each triangle is 156 inches.
Therefore, the perimeter of each triangle is 156 inches.
