SOLUTION: Hi I can't seem to solve this problem, The lengths in centimeters of two sides of a rectangle are consecutive odd integers. The perimeter is 120 cm. What is the area of the rect

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: Hi I can't seem to solve this problem, The lengths in centimeters of two sides of a rectangle are consecutive odd integers. The perimeter is 120 cm. What is the area of the rect      Log On


   



Question 507617: Hi I can't seem to solve this problem,
The lengths in centimeters of two sides of a rectangle are consecutive odd integers. The perimeter is 120 cm. What is the area of the rectangle
Please be as detailed as possible thanks for your time.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the consecutive odd integers = +n+ and +n%2B2+
( this could be 3 and 5 or 17 and 19 )
If the sides of a rectangle are a and b, then perimeter
+P+=+2a+%2B+2b+
In this case,
+P+=+2n+%2B+2%2A%28n+%2B+2%29+
+120+=+2n+%2B+2n+%2B+4+
+4n+=+116+
+n+=+29+
+n+%2B+2+=+31+
Area = +29%2A31+=+899+
check:
+P+=+2n+%2B+2%2A%28n+%2B+2%29+
+P+=+2%2A29+%2B+2%2A31+
+P+=+58+%2B+62+
+P+=+120+
OK