SOLUTION: The length of a rectangle is 10 feet linger that it is wide. If each side is increased by 10 feet, then the area is multiplied by 3. What was the size of the original rectangle?

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: The length of a rectangle is 10 feet linger that it is wide. If each side is increased by 10 feet, then the area is multiplied by 3. What was the size of the original rectangle?       Log On


   

Question 1027868: The length of a rectangle is 10 feet linger that it is wide. If each side is increased by 10 feet, then the area is multiplied by 3. What was the size of the original rectangle?
The width or the shorter side is
The length or the long side is
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
w and L for width and length;

system%28L=w%2B10%2CwL=A%2CandThenNewDimensions%2CL%2B10=w%2B10%2B10%2Cw%2B10%29

New area,
becomes the old area multiplied by 3:
%28L%2B10%29%28w%2B10%29=3A
wL%2B10w%2B10L%2B100=3wL
-2wL%2B10w%2B10L%2B100=0
wL-5w-5L-20=0
w%28w%2B10%29-5w-5%28w%2B10%29-20=0-----substituted for L
w%5E2%2B10w-5w-5w-50-20=0
w%5E2%2B0-70=0
w%5E2=70
highlight%28w=sqrt%2870%29%29
-
highlight%28L=10%2Bsqrt%2870%29%29