Activity 8: Let's Make a Table!
Study the situation below and answer the questions that follow.
*Mang Jose wants to make a table which has an area of 6 m. The length of the table has to be 1 m longer than the width
a)If the width of the table is p meters, what will be its length?
b)Form a quadratic equation that represents the situation.
c)Without actually computing for the roots, determine whether the dimensions of the table are rational numbers. Explain.
d)Give the dimensions of the table.
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Answer:
A = W * L (Width*Length)
Let W = x and L = y; so
6 = xy
A: 6
y: (x+1)
x: x
a) The length of the table is represented by the equation (x+1).
6=(x+1)x
6=x²+x
b) Quadratic Equation
x²+x-6=0
c) Yes the dimension of the table are RATIONAL numbers.
Solve the quadratic equation for the value of x by factoring
x²-3x-2x-6=0
X(x+3)-2(x+3=0)
(x+3)(x-2)=0
x+3=0
x-2=0
x=-3
x=2
Since dimensions must be positive, x will be 2.
Use 6 = xy to find y
6 = 2y (divide both sides by 2)
6/2=2y/2
y = 3
d) So the dimension of the table is 3m×2m