SOLUTION: If the length of a rectangle increases by 2 cm, its area will increase by 12 cm2. If the width increases by 3 cm, its area will increase by 21cm^2. What is the original area of the

Algebra ->  Rectangles -> SOLUTION: If the length of a rectangle increases by 2 cm, its area will increase by 12 cm2. If the width increases by 3 cm, its area will increase by 21cm^2. What is the original area of the      Log On


   

Question 1063348: If the length of a rectangle increases by 2 cm, its area will increase by 12 cm2. If the width increases by 3 cm, its area will increase by 21cm^2. What is the original area of the rectangle?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
w and L the origina width and length
A the original area

system%28A=wL%2Cw%28L%2B2%29=A%2B12%2C%28w%2B3%29L=A%2B21%29

That is the system to solve.

The second equation:
wL%2B2w=A%2B12
wL%2B2w=wL%2B12
2w=12
w=6

The third equation:
wL%2B3L=A%2B21
wL%2B3L=wL%2B21
3L=21
L=7

Width is 6
Length is 7

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
If the length of a rectangle increases by 2 cm, its area will increase by 12 cm2. If the width increases by 3 cm,
its area will increase by 21cm^2. What is the original area of the rectangle?
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Everything is much easier and simpler than the "josgarithmetic" solution is. 

1.  (L+2)*W - LW = 12.   ( "If the length of a rectangle increases by 2 cm, its area will increase by 12 cm2" )  --->

    LW + 2W - LW = 12  --->  2W = 12  --->  W = 12%2F2 = 6 cm.


2.  L*(W+3) - LW = 21    ( "If the width increases by 3 cm, its area will increase by 21cm^2." )  --->  

    LW + 3L - LW = 21  --->  3L = 21  --->  L = 21%2F3 = 7 cm.

Answer.  L = 7 cm,  W = 6 cm.

Solved.