SOLUTION: If the length of a rectangle is increased by 12 and the width is decreased by 8,the area is unchanged.The area is also unchanged if the original legth is increased by 5 and the or

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: If the length of a rectangle is increased by 12 and the width is decreased by 8,the area is unchanged.The area is also unchanged if the original legth is increased by 5 and the or      Log On


   

Question 105985: If the length of a rectangle is increased by 12 and the width is decreased by 8,the area is unchanged.The area is also unchanged if the original legth is increased by 5 and the original width is decreased by 4 .Find the original dimensions of the rectangle.
Answer by alvinjohnburgos(11) About Me  (Show Source):
You can put this solution on YOUR website!
if L = length of triangle
W = width of triangle
Then the area of the triangle would be:
eq.1)A+=+LW
the length of a rectangle is increased by 12 and the width is decreased by 8,the area is unchanged:
eq.2)A+=+%28L+%2B+12%29%28W+-+8%29
The area is also unchanged if the original length is increased by 5 and the original width is decreased by 4:
eq.3)A+=+%28L+%2B+5%29%28W+-+4%29
Substituting LW for A in eq2:
LW+=+%28L+%2B+12%29%28W+-+8%29
LW+=+LW++-+8L++%2B+12W+-+96
12W+-+8L+=+96
12W+=+96+%2B+8L
W+=+8+%2B+%282%2F3%29L
Substituting LW for A and (8 + (2/3)L) for W in eq3:
L%288+%2B+%282%2F3%29L%29+=+%28L+%2B+5%29%288+%2B+%282%2F3%29L+-+4%29
8L+%2B+%282%2F3%29L%5E2+=+%28L+%2B+5%29%284+%2B+%282%2F3%29L%29
8L+%2B+%282%2F3%29L%5E2+=+4L+%2B+%282%2F3%29L%5E2+%2B+20+%2B+%2810%2F3%29L
%282%2F3%29L+=+20
L+=+30
W+=+8+%2B+%282%2F3%29L
W+=+8+%2B+%282%2F3%29%2830%29
W+=+8+%2B+20+=+28
Dimensions of the triangle:
length is 30 units
width is 28 units
area is 840 square units