SOLUTION: if the length of a certain rectangle was decreased by 6 feet and the width increased by 8 feet, the area would remain the same. also the area would remain unchanged if the length w

Algebra ->  Rectangles -> SOLUTION: if the length of a certain rectangle was decreased by 6 feet and the width increased by 8 feet, the area would remain the same. also the area would remain unchanged if the length w      Log On


   

Question 798837: if the length of a certain rectangle was decreased by 6 feet and the width increased by 8 feet, the area would remain the same. also the area would remain unchanged if the length was increased by 6 feet and the width decreased by 4 feet. find the dimensions of the rectangle.
Answer by Finavon(81) About Me  (Show Source):
You can put this solution on YOUR website!
Area = length x breadth
Here Area = a*b = (a-6)*(b+8) = (a+6)*(b-4)
ab = ab+8a-6b-48 = ab-4a+6b-24
Subtract ab from each
4a=3b+24
And
4a=6b-24
These are equal
3b+24=6b-24
48=3b
b=16
a=18
Rectangle is 18 x 16 ft
Check
Area1=16*18=72*4
Area2=12*24
Area3=24*12