SOLUTION: The ratio of length to width in a rectangle is 3 to 1. If the perimeter of the rectangle is 152 feet, what is the length of the rectangle? Select one: a. 57 feet b. 76 feet c.

Algebra ->  Length-and-distance -> SOLUTION: The ratio of length to width in a rectangle is 3 to 1. If the perimeter of the rectangle is 152 feet, what is the length of the rectangle? Select one: a. 57 feet b. 76 feet c.      Log On


   

Question 1058395: The ratio of length to width in a rectangle is 3 to 1. If the perimeter of the rectangle is 152 feet, what is the length of the rectangle?
Select one:
a. 57 feet
b. 76 feet
c. 114 feet
d. 38 feet
Found 2 solutions by josmiceli, jim_thompson5910:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+L+%2F+W+=+3+%2F+1+
(1) +L+=+3W+
----------------
+2L+%2B+2W+=+152+
(2) +L+%2B+W+=+76+
-------------------
Plug (1) into (2)
(2) +3W+%2B+W+=+76+
(2) +4W+=+76+
(2) +W+=+19+
and
(1) +L+=+3W+
(1) +L+=+3%2A19+
(1) +L+=+57+
--------------------
(a) The length is 57 ft

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
"The ratio of length to width in a rectangle is 3 to 1" means L%2FW=3%2F1 leading to L+=+3W after we solve for L

In other words, the length is three times longer than the width.

" the perimeter of the rectangle is 152 feet" so P = 152

---------------------------------------------------------------------------------------------------------

Perimeter of a rectangle:


P+=+2%2AL%2B2%2AW


P+=+2%2A3W%2B2%2AW Replace L with 3W. This works because we found earlier that L+=+3W


152+=+2%2A3W%2B2%2AW Replace P with 152; now we solve for W


152+=+6W%2B2W


152+=+8W


8W+=+152


8W%2F8+=+152%2F8


W+=+19


The width is 19 feet


Use this to find the length


L+=+3W


L+=+3%2A19 Replace W with 19


L+=+57


and the length is 57 feet

Therefore, the final answer is choice A) 57 feet