Mr.bonifacio cuts different sizes of rectangular plywood to be used in the furniture that he makes some of these rectangular plywood are described below.
plywood 1: the length of the plywood is twice its width and the area is 4.5 sq ft.
plywood 2: the length of the plywood is 1.4ft less than twice its width and the area is 16 sq ft.
plywood 3: the perimeter of the plywood is 10ft and its area is 6sq ft.
Questions:
1.What Quadratic equation represents the area of each piece of plywood?Write the equation in terms of the width of the plywood?
2.write each equation formulated in item form then determine the value of a,b,c?
3.Solve each equation using the quadratic formula?

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Answers

2014-07-06T22:20:16+08:00

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Plywood1:   x = width   ;   length = 2x

1)  x (2x) = 4.5
2)  2x² - 4.5 = 0
    a = 2  ;  b = 0   ;  c = -4.5 
3) x = \frac{-b \pm\sqrt{b^2-4ac} }{2a} = \frac{0 \pm\sqrt{0-4(2)(-4.5)} }{2(2)}= \frac{\pm6}{4} = \boxed{\frac{3}{2}}


Plywood2:   x = width   ;   length = 2x-1.4
1)  x (2x-1.4) = 16
2)  2x² -1.4x -16 = 0
    a = 2   ;   b = -1.4   ;   c = -16
3) x = \frac{-b \pm\sqrt{b^2-4ac} }{2a}=\frac{1.4 \pm\sqrt{1.96-4(2)(-16)} } {2(2)}=\frac{1.4 \pm11.4 }{4}=\boxed{3.2}


Plywood3:   x = width   ;   length = 5-x
1)  x (5-x) = 6
2)  -x² +5x -6 = 0
    a = -1    ;   b = 5   ;   c = -6
3) x = \frac{-b \pm\sqrt{b^2-4ac} }{2a}=\frac{-5 \pm\sqrt{25-4(-1)(-6)} }{2(-1)}=\frac{-5 \pm1}{-2}
\boxed{x_1=3}
\boxed{x_2=2}

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