Question

Find the perimeter of rectangle BCEF. Round your answer to the nearest hundredth
A(-5, 4)
B(0, 3)
F(-2, 1)
-4 -2
6
x
C(4, -1)
1
E(2, -3)
D(4, -5)

Answer 1

Answer:

The perimeter of the rectangle B C E F is 16.97 units

Step-by-step explanation:

* Lets explain how to solve the problem

- B C E F is a rectangle

- The perimeter of the rectangle is the sum of the length of its

 four sides

 

- The coordinates of the vertices of the rectangle are:

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

- To find the dimensions of the rectangle use the rule of distance

  d = $\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$

* Lets solve the problem

∵ $(BC)=\sqrt{(4-0)^{2}+(-1-3)^{2}}=\sqrt{16+16}=\sqrt{32}$

∵ $(CE)=\sqrt{(2-4)^{2}+(-3--1)^{2}}=\sqrt{4+4}=\sqrt{8}$

∵ $(FE)=\sqrt{(2--2)^{2}+(-3-1)^{2}}=\sqrt{16+16}=\sqrt{32}$

∵ $(BF)=\sqrt{(-2-0)^{2}+(1-3)^{2}}=\sqrt{4+4}=\sqrt{8}$

∵ The perimeter of the rectangle = BC + CE + FE + BF

∴ The perimeter = $\sqrt{32}+\sqrt{8}+\sqrt{32}+\sqrt{8}=16.97$

∴ The perimeter of the rectangle B C E F is 16.97 units