The length of a rectangle is 12 units longer than the width. the perimeter is 7 times the width. find the length and the width of the rectangle?

Log explanation below; answer is at bottom.

If the length, l, is 12 units longer than the width, w, then w = l - 12. If the perimeter, p,

p = 2l +2w,

is 7 x w, then

w = p/7

When two things are set equal to the same variable, they are equal to each other, so,

l - 12 = p/7

Now you need to get rid of the p so you are only working with one variable. To do this you plug in whatever p is equal to for p, so,

l - 12 = (2l + 2w)/7 now to get rid of the w do the same thing we did with p just for w. So,

l - 12 = (2l + 2(l - 12))/7

To solve this you want to multiply both sides by 7 first to get rid of the fraction.

7l - 84 = 2l + 2(l - 12)

Next you want to distribute the 2 over the l and the 12.

7l - 84 = 2l + 2l - 24

Next you want to combine like terms on each side.

7l - 84 = 4l - 24

Next add 84 and subtract 4l from sides to isolate the variable.

3l = 60

Now divide each side by 11 to get your answer.

l = 20.

To find the width,

w = l - 12  

Just plug in and solve.

w = 20 - 12

w = 8

So your length and width are 20 and 8.

l = 20

w = 8

i think it would be 43 movies that would have to be watched.

step-by-step explanation:

think about it. for the second plan, every month is 8 dollars. 8 x 12= 96. so thats the number for the second plan. now for the first plan, its annual meaning you have to pay 10 dollars every year. so now you have to get an equivalent amount of 86 since 96-10=86. 86 divided by 2 since every movie costs 2$ then you would have to watch 43 movies a year to get the same as the second plan. i really hoped this . have a wonderful day as well!

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step-by-step explanation: