SOLUTION: The perimeter of a rectangle is 76 cm. if the width is doubled and the length is halved, the new rectangle has a perimeter of 62 cm. What are the dimensions of the original rectang

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: The perimeter of a rectangle is 76 cm. if the width is doubled and the length is halved, the new rectangle has a perimeter of 62 cm. What are the dimensions of the original rectang      Log On


   

Question 1009896: The perimeter of a rectangle is 76 cm. if the width is doubled and the length is halved, the new rectangle has a perimeter of 62 cm. What are the dimensions of the original rectangle and what is the area of the new rectangle?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The formula for perimeter is:
(1) +76+=+2L+%2B+2W+
Also given:
(2) +62+=+2%2A%28L%2F2%29+%2B+2%2A%28+2W+%29+
---------------------------
(2) +62+=+L+%2B+4W+
and
(1) +76+=+2L+%2B+2W+
(1) +38+=+L+%2B+W+
-------------------
Subtract (1) from (2)
(2) +62+=+L+%2B+4W+
(1) +-38+=+-L+-+W+
--------------------
+24+=+3W+
+W+=+8+
and
(1) +38+=+L+%2B+W+
(1) +38+=+L+%2B+8+
(1) +L+=+30+
The dimensions of the original rectangle are:
8 x 30
------------------
The area of the new rectangle is:
+A+=+%28+L%2F2+%29%2A%28+2W+%29+
+A+=+15%2A16+
+A+=+240+
240 cm2