Question

40 POINTS

Answer 1

we know that

The area of a rectangle is equal to

$A=L*W$

where

L is the length side of the rectangle

W is the width side of the rectangle

The perimeter of the rectangle is equal to

$P=2L+2W$

Step $1$

Find the dimensions of the rectangles

we know that

the distance between two points is equal to the formula

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

Find the distance A-F

A-F is the width of the rectangles ABEF and ACDF

$A(0,6)\\F(5,2)$

substitute the values in the formula

$dAF=\sqrt{(2-6)^{2}+(5-0)^{2}}$

$dAF=\sqrt{(-4)^{2}+(5)^{2}}$

$dAF=\sqrt{41}\ units$

so

$W=\sqrt{41}\ units$

Find the distance F-E

F-E is the length side of the rectangle ABEF

$F(5,2)\\E(11,10)$

substitute the values in the formula

$dFE=\sqrt{(10-2)^{2}+(11-5)^{2}}$

$dFE=\sqrt{(8)^{2}+(6)^{2}}$

$dFE=10\ units$

Find the distance F-D

F-D is the length side of the rectangle ACDF

$F(5,2)\\D(14,14)$

substitute the values in the formula

$dFD=\sqrt{(14-2)^{2}+(14-5)^{2}}$

$dFD=\sqrt{(12)^{2}+(9)^{2}}$

$dFD=15\ units$  

Step $2$

the dimensions of the rectangle ABEF are

$L=10\ units\\W=\sqrt{41}\ units$

Find the area of the rectangle ABEF

$A=10*\sqrt{41}=10\sqrt{41}\ units^{2}$

$A=64.03\ units^{2}$

Step $3$

the dimensions of the rectangle ACDF are

$L=15\ units\\W=\sqrt{41}\ units$

Find the area of the rectangle ACDF

$A=15*\sqrt{41}=15\sqrt{41}\ units^{2}$

$A=96.05\ units^{2}$

Step $4$

The ratio of the area of rectangle ABEF to the area of rectangle ACDF is

$(10\sqrt{41}/15\sqrt{41})=(10/15)=2/3$

Step $5$

Find the perimeter of the rectangle BCDE

we know that

$W=\sqrt{41}\ units$

the length of the rectangle BCDE is equal to the distance E-D

$ED=FD-FE$

$ED=15-10=5\ units$

$L=5\ units$

$P=2*5+2*\sqrt{41}=22.81\ units$

therefore

the answer part a) is

$2:3$

the answer part b) is

the area of the rectangle ABEF is $64.03\ units^{2}$

the answer part c) is  

the area of the rectangle ACDF is $96.05\ units^{2}$

the answer Part d) is  

the perimeter of the rectangle BCDE is $22.81\ units$

Answer 2

Answer:

1.) 2:3

2.) 64.03

3.) 96.05

4.) 22.81