Area of square = s^2
Area of Rectangle = lw
l = 2s
w+3 = s
solve for w, w=s-3
Now we have l and w.
Plug both into area of rectangle formula so: (2s)(s-3)
Since both areas are equal set both equations equal to each other:
(2s)(s-3)=s^2
Now simplify
2s^2-6s=s^2
s^2-6s=0, Solve for s.
Factor polynomial. s(s-6)=0 , s can be equal to 0 or 6. HOWEVER, you cannot have a side length of 0 therefore the side length has to be 6.
Now plug in s for the length formula for the rectangle:
l = 2s so... l = 2(6) so length of rectangle = 12.
Now plug in s for the width formula for the rectangle:
w+3=s so... w+3=6 so width of rectangle = 3.
Now the dimensions of the rectangle are 12 by 3. 12 being length and 3 width.
To CHECK:
Find area of rectangle:
A=lw so A=3 times 12 so A=36
Find area of square:
We know the side is equal to 6 so
A=s^2 so 6^2 = 36
The areas are equal that verifies the answer of 12 by 3.
multiply 40 by 30% to find the discount then subtract
40 * 0.30 = 12
40-12 = 28
they would cost $28
ANSWER
Find out the expression gives the percent of survey participants who chose swimming.
To proof
As given
75 girls at a summer camp were asked to complete a survey about their favorite outdoor activity.
27 girls chose swimming
32 girls chose hiking.
FORMULA

total girls = 75
girls chose swimming = 27
put in the formula

= 36%
36% of survey participants who chose swimming
Hence proved
Answer
Find out how much money did she start with.
To proof
let us assume that the money she had be x.
As given
woman spent two thirds of her money

Money she had after spent two thirds of her money = Total money - money spent


As given she lost two thirds the remainder


we get

Money she had after lost two thirds the remainder = Money she had after spent two thirds of her money - she lost two thirds the remainder


As given
she had $4 left
thus

x = $36
she start with $36.
Hence proved