Question

Find the perimeter of rectangle BCEF. Round your answer to the nearest hundredth DI AC-5, 4) B(0, 3) 2 F(-2, 1) -4 -2 2 4 C(4, -1) 2 -4 E(2, -3) D(4, -5) 6 The perimeter is about units

Answer 1

Let's start by listing out the vertices of the rectangle BCEF

B (0, 3), C (4, -1) , E (2, -3) , F (-2, 1)

The formula for perimeter of a rectangle is given by:

`P=2\left(l+w\right)`

To calculate the distances BC, CE, EF & FB, we will use the formula for distance between two points:

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`
`\begin{gathered} |BC|=√((4-0)^2+(-1-3)^2)=√(16+16)=√(32) \\ |CE|=√((2-4)^2+(-3--1)^2)=√(4+4)=√(8) \\ \text{the opposite sides of rectangles are the same} \\ |BC|\equiv|FE|,|CE|\equiv|BF| \end{gathered}`
`\begin{gathered} P=2(l+w) \\ P=2(√(32)+√(8)) \\ P=16.97units \end{gathered}`

Perimeter of the rectangle BCEF is 16.97 units