Question 1076979: The length of a rectangle is 3 times its width. If the width is doubled and the length is increased by 1, the area is increased by 56.
Represent the length in terms of the width: Length = ______
Represent the area of the original rectangle using w and the expression from part a.
Area of original rectangle = ________________
Represent the width of the new rectangle. Width of new rectangle = _____
Represent the length of the new rectangle. Length of new rectangle = _______
Represent the area of the new rectangle. Area of the new rectangle = _________
Distribute in the equation from part e to get a quadratic equation: ___________________
Write the equation that compares the areas of the old and new rectangles:
___________________________________= ________________________________
Combine like terms and write the equation in standard form.
___________________________________________________________
a = _____ b = ______ c = _______
Plug the values from part i into the quadratic formula:
Simplify and solve. Show your work.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! width is x, length ix 3x, area is 3x^2
2x*(3x+1)=6x^2+2x, and subtract 56=3x^2, the original area
3x^2+2x-56=0
a=3, b=2, c=-56
x=(1/6)(-2+/- sqrt(4+672)); sqrt 676=26
x=(1/6)(24), take positive root only, and x=4
width 4
length is 12
area is 48
width 8 and length 13, area is 104, which is 56 more.
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