SOLUTION: the length of a rectangle is 3cm greater than the width.if each dimension is increased by 2cm,the areais increased by 26cm^2.find the original dimensions of the rectangle?

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Question 159750: the length of a rectangle is 3cm greater than the width.if each dimension is increased by 2cm,the areais increased by 26cm^2.find the original dimensions of the rectangle?
Answer by KnightOwlTutor(293) About Me  (Show Source):
You can put this solution on YOUR website!
Original dimensions
X=width
x+3=length
New dimensions
X+2=width
X+5=length
The area of a rectangle is W*L
the change in the dimensions increased the area of the original rectangle by 26
Orignal area +26=New Area
X(X+3)+26=(X+2)(X+5)
Use distributive and Foil method
x^2+3X+26=x^2+7X+10
Subtract x^2 from both sides
3X+26=7X+10
Subract 3X from both sides
26=4X+10
Subtract 10 from both sides
16=4X
Divide both sides by 4
4=X
The original dimensions of the rectangle were 4cm X 7cm
The area is 28cm^2
The new dimensions are 6cm X 9cm
The area is =54cm^2
54cm^2-28cm^2=26cm^2