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The endpoints for one of the sides of a square are (2,4) and (14,9).

The perimeter of the square with the given endpoints is ____ units, and the area of the square is ____ square units.

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Perimeter of the square is 52 units and area of the square is 169 sq. units

Step-by-step explanation:

  • Step 1: Given the coordinates of the endpoints are (2, 4) and (14, 9). Find the distance between the two to find the length of the side.

Length of the side = √(x2 - x1)² + (y2 - y1)²

                               = √(14 - 2)² + (9 - 4)² = √12² + 5²

                               = √144 + 25 = √169 = 13 units

  • Step 2: Find the perimeter of the square.

Perimeter = 4 × side length of the square

                 = 4 × 13 = 52 units

  • Step 3: Find the area of the square.

Area = (side)² = 13² = 169 sq. units

Answer:

Perimeter of the square= 52

Step-by-step explanation:

The points of one side of the square are: [tex](2,4)[/tex] and [tex](14,9)[/tex]

Finding the side of the square using the Distance Formula:

          [tex]Side=\sqrt{(14-2)^2+(9-4)^2}\\\\ =\sqrt{12^2+5^2}\\\\ =\sqrt{144+25}\\\\ =\sqrt{169}\\\\ =13[/tex]

Side of the square with the given coordinates is '13'

Perimeter of the square = 4*Side= 4*13= 52

              =52

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