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. -show all work! -

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 . 

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









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




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


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