SOLUTION: The length of a rectangle is 3cm more than the width. if the width is increased by 2cm. and the length decreased by1cm., the figure becomes a square with an area of 81 sq. cms. wha

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Question 1005117: The length of a rectangle is 3cm more than the width. if the width is increased by 2cm. and the length decreased by1cm., the figure becomes a square with an area of 81 sq. cms. what is the original perimeter of the rectangle
Answer by addingup(3677) About Me  (Show Source):
You can put this solution on YOUR website!
(w+3-1)(w+2)= 81
(w+2)(w+2)= 81 now FOIL
w^2 First
2w Outer
2w Inner
4 Last
Now we have:
w^2+2w+2w+4
= w^2+4w+4= 81 write the left side as a square
(w+2)^2= 81 take the square root of both sides:
w+2= 9 or w+2= -9
We can't use the negative, toss it out. Our answer is:
w= 9 This is the width of the rectangle, and the length is:
l= 9+3= 12
Perimeter: 2l+2w
2(12)+2(9)= 24+18= 42 is the original perimeter of the rectangle