Question

Square LAMP has vertices L(-2, -3), A(4, -1), M(2,5), and P(-4, 3). What is the

perimeter of the square?

Answer 1

The perimeter of the square LAMP is 8
`√(10)` units

Explanation:

The rule of the distance between two points (x1, y1) and (x2, y2) is

d =
`\sqrt{(x2-x1)^(2)+(y2-y1)^(2)}`

∵ LAMP is a square

∵ The sides of the square are equal in lengths

∴ LA = AM = MP = PL

Let us find the length of one side of it

∵ L = (-2, -3) and A = (4, -1)

∴ x1 = -2 and y1 = -3

∴ x2 = 4 and y2 = -1

→ Substitute them in the rule of the distance above to find LA

∵ LA =
`\sqrt{(4 - -2)^(2)+(-1--3)^(2)}`

∴ LA =
`\sqrt{(4+2)^(2)+(-1+3)^(2)}`

∴ LA =
`\sqrt{(6)^(2)+(2)^(2)}`

∴ LA =
`√(36+4)` =
`√(40)`

→ Simplify the root

∴ LA = 2
`√(10)` units

∵ The perimeter of the square = 4 × side

∴ The perimeter of the square = 4 × 2
`√(10)`

∴ The perimeter of the square = 8
`√(10)`

∴ The perimeter of the square LAMP is 8
`√(10)` units