Question

find the perimeter of △cde. round your answer to the nearest hundredth.
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 $CD$

For points $C(4,-1)$ and $D(4,-5)$, $x_1 = 4,y_1=-1,x_2 = 4,y_2=-5$. Then $d_{CD}=\sqrt{(4 - 4)^2+(-5+1)^2}=\sqrt{0 + (-4)^2}=4$.

Step3: Calculate length of $DE$

For points $D(4,-5)$ and $E(2,-3)$, $x_1 = 4,y_1=-5,x_2 = 2,y_2=-3$. Then $d_{DE}=\sqrt{(2 - 4)^2+(-3 + 5)^2}=\sqrt{(-2)^2+2^2}=\sqrt{4 + 4}=\sqrt{8}=2\sqrt{2}\approx2.83$.

Step4: Calculate length of $EC$

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

Step5: Calculate perimeter

$P=d_{CD}+d_{DE}+d_{EC}=4 + 2\sqrt{2}+2\sqrt{2}=4 + 4\sqrt{2}\approx4+4\times1.414 = 4+5.656=9.66$.

Answer:

$9.66$