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

perimeter of the square?

1 Answer

1 vote

Answer:

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

User Therobyouknow
by
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