Question

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.

Answer 1

Perimeter of the square= 52

Explanation:

The points of one side of the square are:
`(2,4)` and
`(14,9)`

Finding the side of the square using the Distance Formula:

`Side=√((14-2)^2+(9-4)^2)\\\\ =√(12^2+5^2)\\\\ =√(144+25)\\\\ =√(169)\\\\ =13`

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

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

=52

Answer 2

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

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