Question

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

Answer 1

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

$P=2(x+y)$

$P=44\ cm$

so

$44=2(x+y)$

simplify

$22=x+y$ -----> equation A

The width of a rectangle is one more than twice its length

so

$y=2x+1$ ----> equation B

substitute equation B in equation A

$22=x+(2x+1)$

solve for x

$3x+1=22\\3x=21\\x=7$

therefore

The length is 7 cm

Part 2)  we know that

The simple interest formula is equal to

$I=P(rt)$

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

$t=1\ year\\ P=\ 1,100\\ I=\ 121\\r=?$

substitute in the formula above

$121=1,100(r*1)$

solve for r

$121=1,100(r)$

$r=121/1,100\\r=0.11$

Convert to percentage (Multiply by 100)

$r=0.11*100=11\%$