SOLUTION: A square and a rectangle have the same perimeter. The length of the rectangle is 4 cm less than twice the side of the square, and the width of the rectangle is 6 cm less than the s

Algebra ->  Equations -> SOLUTION: A square and a rectangle have the same perimeter. The length of the rectangle is 4 cm less than twice the side of the square, and the width of the rectangle is 6 cm less than the s      Log On


   

Question 1050410: A square and a rectangle have the same perimeter. The length of the rectangle is 4 cm less than twice the side of the square, and the width of the rectangle is 6 cm less than the side of the square. Find the perimeter of each figure.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = the side of the square
Let +L+ = the length of the rectangle
Let +W+ = the width of the rectangle
--------------------------------------
+L+=+2s+-+4+ cm
+W+=+s+-+6+ cm
+4s+=+2L+%2B+2W+ cm
--------------------
+2s+=+L+%2B+W+
By substitution:
+2s+=+2s+-+4+%2B+s+-+6+
+0+=+s+-+10+
+s+=+10+
and
+L+=+2s+-+4+
+L+=+2%2A10+-+4+
+L+=+16+
and
+W+=+s+-+6+
+W+=+10+-+6+
+W+=+4+
--------------------
The perimeter of the square is:
+4s+=+4%2A10+
+4s+=+40+ cm
The perimeter of the rectangle is:
+2L+%2B+2W+=+2%2A16+%2B+2%2A4+
+2L+%2B+2W+=+32+%2B+8+
+2L+%2B+2W+=+40+ cm