Question

find the perimeter of rectangle bcef. round your answer to the nearest hundredth. a(-5, 4) b(0, 3) f(-2, 1) c(4, -1) e(2, -3) d(4, -5) the perimeter is about units.

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Calculate length of $BC$

For points $B(0,3)$ and $C(4, - 1)$, $x_1 = 0,y_1=3,x_2 = 4,y_2=-1$. Then $BC=\sqrt{(4 - 0)^2+(-1 - 3)^2}=\sqrt{16 + 16}=\sqrt{32}=4\sqrt{2}\approx5.66$.

Step3: Calculate length of $CE$

For points $C(4,-1)$ and $E(2,-3)$, $x_1 = 4,y_1=-1,x_2 = 2,y_2=-3$. Then $CE=\sqrt{(2 - 4)^2+(-3+1)^2}=\sqrt{4 + 4}=\sqrt{8}=2\sqrt{2}\approx2.83$.

Step4: Calculate perimeter of rectangle

The perimeter $P$ of a rectangle is $P = 2(l + w)$. Here $l = BC$ and $w = CE$. So $P=2(4\sqrt{2}+2\sqrt{2})=2\times6\sqrt{2}=12\sqrt{2}\approx16.97$.

Answer:

$16.97$