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Quadratic Equation Word Problem To Expression - Area and Border

Level 1

The topics in this unit focus on constructing and solving quadratic equations from word problems. Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

WorksheetView

Quadratic Equation Word Problem To Expression - Area and Border Worksheet

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Quadratic Equation Word Problem To Expression - Area and Border
1
A 10 by 3 garden has a ditch of width x on all sides. Its total area, including the ditch is 1.
What equation gives the area of the garden?
a A LaTex expression showing 1 = (2 times 10 + x) times (2 times 3 + x)
b A LaTex expression showing 1 = (10 + 2x) times (3 + 2x)
2
A 7 by 10 garden has a ditch of width x on all sides. Its total area, including the ditch is 1.
What equation gives the area of the garden?
a A LaTex expression showing 1 = (7 - x over 2 ) times (10 - x over 2 )
b A LaTex expression showing 1 = (7 + 2x) times (10 + 2x)
c A LaTex expression showing 1 = (2 times 7 + x) times (2 times 10 + x)
3
A 11 by 3 painting has a border of width x on all sides. Its total area (border included) is 1.
What equation gives the area of the painting?
a A LaTex expression showing 1 = (11 over 2 - x) times (3 over 2 - x)
b A LaTex expression showing 1 = (11 + 2x) times (3 + 2x)
4
A 7 by 11 painting has a border of width x on all sides. Its total area (border included) is 1.
What equation gives the area of the painting?
a A LaTex expression showing 1 = (7 + 2x) times (11 + 2x)
b A LaTex expression showing 1 = (7 over 2 - x) times (11 over 2 - x)
c A LaTex expression showing 1 = (7 - 2x) times (11 - 2x)
5
A 4 by 11 garden has a ditch of width x on all sides. Its total area, including the ditch is 1.
What equation gives the area of the garden?
a A LaTex expression showing 1 = (4 + 2x) times (11 + 2x)
b A LaTex expression showing 1 = (2 times 4 + x) times (2 times 11 + x)
c A LaTex expression showing 1 = (4 over 2 - x) times (11 over 2 - x)
6
A 5 by 6 garden has a ditch of width x on all sides. Its total area, including the ditch is 1.
What equation gives the area of the garden?
a A LaTex expression showing 1 = (5 - 2x) times (6 - 2x)
b A LaTex expression showing 1 = (5 + 2x) times (6 + 2x)
c A LaTex expression showing 1 = (2 times 5 + x) times (2 times 6 + x)
7
A 2 by 9 garden has a ditch of width x on all sides. Its total area, including the ditch is 1.
What equation gives the area of the garden?
a A LaTex expression showing 1 = (2 - x over 2 ) times (9 - x over 2 )
b A LaTex expression showing 1 = (2 over 2 - x) times (9 over 2 - x)
c A LaTex expression showing 1 = (2 + 2x) times (9 + 2x)
8
A 11 by 6 garden has a ditch of width x on all sides. Its total area, including the ditch is 1.
What equation gives the area of the garden?
a A LaTex expression showing 1 = (11 - x over 2 ) times (6 - x over 2 )
b A LaTex expression showing 1 = (11 + 2x) times (6 + 2x)