SOLUTION: The area of a rectangle is {{{ 270cm^2 }}}. If the shorter side was reduced by 2cm and the longer side was increased by {{{ 16cm^2 }}}. Find the lengths of the sides of the origina

Algebra ->  Expressions -> SOLUTION: The area of a rectangle is {{{ 270cm^2 }}}. If the shorter side was reduced by 2cm and the longer side was increased by {{{ 16cm^2 }}}. Find the lengths of the sides of the origina      Log On


   

Question 824617: The area of a rectangle is +270cm%5E2+. If the shorter side was reduced by 2cm and the longer side was increased by +16cm%5E2+. Find the lengths of the sides of the original rectangle.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
You omitted a piece of data. Let us say the longer side is increased by a positive k amount. We could then say shorter side is x-2 and longer side is y+k.

Originally, xy=270. Later, through length changes, %28x-2%29%28y%2Bk%29=16.
Change equation is also %28xy-2y%2Bkx-2k%29=16, and knowing xy=270, this means 270-2y%2Bk%28x-2%29=16
260-2y%2Bk%28x-2%29=0

Try again, giving by how much was longer side increased.

Watch your problem description carefully. To say that the longer side is increased by 16cm%5E2 is wrong. You must really mean, "increased by 16 cm".