A triangular piece of fabric has side lengths of 3 inches, 4 inches, and 5 inches. Will it fit in the corner of a rectangular quilt? Explain.
Yes, because it is a right triangle.
Yes, because it is an isosceles triangle.
No, because it is an equilateral triangle.
No, because it is an obtuse triangle.
Yes, because it is a right triangle.
The side lengths of 3 inches, 4 inches, and 5 inches form a right triangle. This is due to the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side, which is 5 inches) is equal to the sum of the squares of the other two sides (3 inches and 4 inches). Since this triangle fits perfectly with the dimensions of a right triangle, it will fit into a rectangular quilt corner.