Answer:
The dimensions of rectangle are 5 m x 6 m
Step-by-step explanation:
Let
x -----> the length of rectangle
y ----> the width of rectangle
we know that
The area of a rectangle is
[tex]A=xy[/tex]
[tex]A=30\ m^2[/tex]
so
[tex]30=xy[/tex] -----> equation A
The perimeter of a rectangle is
[tex]P=2(x+y)[/tex]
[tex]P=22\ m[/tex]
so
[tex]22=2(x+y)[/tex]
simplify
[tex]11=(x+y)[/tex]
isolate the variable y
[tex]y=11-x[/tex]-----> equation B
we have
[tex]30=xy[/tex] -----> equation A
[tex]y=11-x[/tex]-----> equation B
Substitute equation B in equation A
[tex]30=x(11-x)[/tex]
[tex]30=-x^2+11x[/tex]
[tex]x^2-11x+30=0[/tex]
Solve the quadratic equation by graphing
using a graphing tool
the solution is x= 5 or x=6
see the attached figure
Find out the value of y
For x=5
[tex]y=11-5=6[/tex]
For x=6
[tex]y=11-6=5[/tex]
therefore
The dimensions of rectangle are 5 m x 6 m
