The width of a rectangle is one more than twice its length. If the rectangle's perimeter is 44 cm, then its length is ____ cm.


$1,100 invested for one year pays a return of $121. What is the rate of return?


Must answer both questions or I will report your answer

Respuesta :

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]

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