Answer:
a) x = 16 and y = 6
b) P = 864 in
Step-by-step explanation:
a)
The opposite sides of the rectangle are of equal length.
Therefore we have the system of equations:
[tex]\left\{\begin{array}{ccc}3y=2+x&\text{subtract 2 from both sides}\\3x=2+x+5y&\text{subtract x from both sides}\end{array}\right\\\\\left\{\begin{array}{ccc}3y-2=x&(*)\\2x=2+5y&(**)\end{array}\right[/tex]
Substitute from (*) to (**):
[tex]2(3y-2)=2+5y\qquad\text{use distributive property}\\\\(2)(3y)+(2)(-2)=2+5y\\\\6y-4=2+5y\qquad\text{add 4 to both sides}\\\\6y=6+5y\qquad\text{subtract 5y from both sides}\\\\\boxed{y=6}[/tex]
Put the value of y to (*):
[tex]x=3(6)-2\\\\x=18-2\\\\\boxed{x=16}[/tex]
b)
Calculate the width and the length:
[tex]3x = 3(16) = 48\\\\3y = 3(6) = 18[/tex]
The perimeter:
[tex]P = 2w + 2l\\\\P = (48)(18)=864\ in[/tex]
