SOLUTION: 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

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
Answer by Mathpassionate(25) (Show Source): You can put this solution on YOUR website!
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.

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