Question 538628
the perimeter of a rectangle is 60 feet. the ratio of the width to the length is three to seven. find the area of this rectangle


A = Area
W = Width
L = Length
P = Perimeter


We know that:

1) A = L*W
2) P = 2L + 2W


Information provided:

P = 60

W/L = 3/7



Work out the value of W.


W = 3L/7


Now, let's substitute  W = 3L/7 into the equation P = 2L + 2W



P = 2L + 2W
P = 2L + 2*(3L/7)
P = 2L + 6L/7


We know that P = 60


P = 2L + 6L/7
60 = 2L + 6L/7
60 = 14L/7 + 6L/7
60 = (14L+6L)/7
60 = (20L)/7
60*7 = 20L
(60*7)/20 = L
3*7 = L
21 = L



Now, let's substitute  L =21 into the equation W = 3L/7


W = 3L/7
W = 3*21/7
W = 3*3
W = 9



Now using:


A = L*W
A = 21*9
A = 189



The answer is:

The area of the rectangle is 189 Square feet.




If you have any questions, please let me know.