SOLUTION: the length of a rectangle is three times as long as the width. If each side is increased by 6, the area of the new rectangle is 156 more than the area of the original rectangle. Wh

Algebra ->  Rectangles -> SOLUTION: the length of a rectangle is three times as long as the width. If each side is increased by 6, the area of the new rectangle is 156 more than the area of the original rectangle. Wh      Log On


   

Question 739956: the length of a rectangle is three times as long as the width. If each side is increased by 6, the area of the new rectangle is 156 more than the area of the original rectangle. What are the dimensions of the new rectangle?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The 1st rectangle is:
+L+=+3W+
-----------------
The 2nd rectangle:
+%28+L+%2B+6+%29%2A%28+W+%2B+6+%29+=+L%2AW+%2B+156+
+L%2AW+%2B+6W+%2B+6L+%2B+36+=+L%2AW+%2B+156+
+6+W+%2B+6L+=+156+-+36+
+6%2A%28+W+%2B+L+%29+=+120+
+W+%2B+L+=+20+
+L+=+20+-+W+
---------------
Going back to the 1st rectangle,
+20+-+W+=+3W+
+4W+=+20+
+W+=+5+
and
+L+=+3W+
+L+=+15+
------------
And, referring to the 2nd rectangle,
+L+%2B+6+=+21+
+W+%2B+6+=+11+
The dimensions of the new rectangle are 11 x 21
----------------
check:
+W+=+5+
+L+=+15+
+L+=+3W+
+15+=+3%2A5+
+15+=+15+
OK
+%28+L+%2B+6+%29%2A%28+W+%2B+6+%29+=+L%2AW+%2B+156+
+%28+15+%2B+6+%29%2A%28+5+%2B+6+%29+=+15%2A5+%2B+156+
+21%2A11+=+75+%2B+156+
+231+=+231+
OK