Question

Examine the diagram and information to answer the question. Rectangle EFGH has vertices at E(7,7), F(1,5), G(2,2), and H(8,4). How many units is the perimeter of rectangle EFGH?

Answer 1

Perimeter of rectangle = 6√10 units (the attachment isnt clear. It seems the answer is in option B)

Explanation:

First we find the distance of the length and width of the rectangle.

Distance between E and F = Distance EF

Distance EF = √(∆y²-∆x²)

= √[(5-7)² + (1-7)²] = √[(-2)² + (-6)²]

= √(4+36) = √40

Distance EF = 2√10

Distance between F and G = Distance FG

Distance FG = √(∆y²-∆x²)

= √[(2-5)² + (2-1)²] = √[(-3)² + (1)²]

= √(9+1) = √10

Distance FG = √10

Length= distance EF = distance HG

And width = distance FG = distance EH

Perimeter of rectangle = 2(length + width)

Perimeter of rectangle = 2(2√10 + √10)

= 2(3√10)

Perimeter of rectangle = 6√10 units (the attachment isnt clear. It seems the answer is in option B)