Final answer:
The distance from one corner of the square to the opposite corner is found by using the Pythagorean theorem on one side of the square. With a perimeter of 20 inches, each side is 5 inches, leading to a diagonal (opposite corner distance) of √50 inches, or approximately 7.07 inches.
Step-by-step explanation:
The question asks about the distance from one corner of the square to the opposite corner. Given that the perimeter of the square is 20 inches, we first need to determine the length of one side of the square. The perimeter (P) of a square is the sum of all its sides, which can be calculated using the formula P = 4s, where 's' represents the side length. Since the perimeter is 20 inches, we divide this by 4 to find the side length: s = 20 inches ÷ 4 = 5 inches.
To find the distance from one corner to the opposite corner, which is the diagonal of the square, we can use the Pythagorean theorem since the square's diagonal forms two right-angled triangles within the square. The formula for the Pythagorean theorem is a² + b² = c², where 'a' and 'b' are the sides of the right-angled triangle, and 'c' is the hypotenuse (the diagonal in this case). Since both sides of the square are equal, the formula simplifies to 5² + 5² = c². Solving for 'c', we get c = √(5² + 5²) = √(25 + 25) = √50, which simplifies to the distance between the opposite corners being √50 inches, or approximately 7.07 inches.