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

Part 1) The length is 7 cm

Part 2) The rate of return is r=11%

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\%`