Answer:
Part 1) The length is 7 cm
Part 2) The rate of return is r=11%
Step-by-step explanation:
Part 1)
Let
x ----> the length of rectangle
y ----> the width of rectangle
we know that
The perimeter of rectangle is equal to
[tex]P=2(x+y)[/tex]
[tex]P=44\ cm[/tex]
so
[tex]44=2(x+y)[/tex]
simplify
[tex]22=x+y[/tex] -----> equation A
The width of a rectangle is one more than twice its length
so
[tex]y=2x+1[/tex] ----> equation B
substitute equation B in equation A
[tex]22=x+(2x+1)[/tex]
solve for x
[tex]3x+1=22\\3x=21\\x=7[/tex]
therefore
The length is 7 cm
Part 2) we know that
The simple interest formula is equal to
[tex]I=P(rt)[/tex]
where
I is the Final Interest Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
in this problem we have
[tex]t=1\ year\\ P=\$1,100\\ I=\$121\\r=?[/tex]
substitute in the formula above
[tex]121=1,100(r*1)[/tex]
solve for r
[tex]121=1,100(r)[/tex]
[tex]r=121/1,100\\r=0.11[/tex]
Convert to percentage (Multiply by 100)
[tex]r=0.11*100=11\%[/tex]