Question

The perimeter of a rectangle is 80 feet. Find the demensions if the length is 5 feet longer than four times the width. Then find the area of the rectangle.

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Answer 1

Hey there!

The first thing we should do is review the formulas for area and perimeter.
Perimeter can be expressed in two ways: a) l+w+l+w OR b) 2l+2w.
The formula for area is: l*w

We know that the length is 5 feet longer than the width, so when we're defining our variables we can say that width is equal to 'w', and length is equal to 4w+5.
Since we know that the perimeter is equal to 80, we can say that
`80= 2(4w+5) + 2(w)`.

Now all we have to do is combine like terms and solve for 80:


`80 = 2(4w+5) +2w`

`80 = 8w + 10 +2w`

`80 = 10w +10`

`80-10 = 10w +10 -10`

`70 = 10w`

`(70)/(10) = (10w)/(10)`

`7 = w`

We now know that the width is equal to 7 feet. To find the length, we can substitute the width into 4w+5:

`l = 4w + 5 = 4(7)+5`

`l = 28 + 5`

`l = 33`

Now we know that the length is equal to 33 feet.

So there's your dimensions: 7ft by 33 ft.

Next, to find the area, we take l*w

`33*7 = 231ft^(2)`


Hope this is helpful! If any of this doesn't make sense or there's more I can help with, please let me know!