Mang jose wants to make a table which has an area of 8 m^2. The length of the table has to be 2 m longer than the width.
1. if the width of the table is p meters what will be its length?
2.form a quadratic equation that represents the situation?
3.find the solution from the given quadratic equation?
4.give the dimension of the table?
what is 2 more than p ?
isn't it p+2 ?
area = p(p+2)
p^2 + 2p = 8
p^2 + 2p - 8 = 0
which factors to
(p+4)(p-2) = 0
p = -4, which is not admissable
or
p = 2
so the table is 2 m by 4 m
check: what is 2 x 4 ?
1. If the width of the table is p meters, then the length can be represented as p + 2 meters.
2. To form a quadratic equation, we need to find the product of the width and length. The area of the table is given as 8 m^2, so we have the equation:
p * (p + 2) = 8
3. To solve the quadratic equation, we can simplify it:
p^2 + 2p - 8 = 0
Factoring the equation, we have:
(p + 4)(p - 2) = 0
Setting each factor equal to zero, we get two possibilities for the width:
p + 4 = 0 -> p = -4 (rejected since width cannot be negative)
p - 2 = 0 -> p = 2
Therefore, the width of the table is 2 meters.
4. Using the width, we can find the length:
Length = Width + 2 = 2 + 2 = 4 meters
The dimensions of the table are:
Width = 2 meters
Length = 4 meters
To answer these questions, let's go step by step:
1. If the width of the table is p meters, we can determine its length by adding 2 meters to the width. So, the length would be p + 2 meters.
2. Now, let's form a quadratic equation that represents the situation. We know that the area of the table is equal to the length multiplied by the width. Therefore, we can write the equation as follows:
Area = length * width
8 m^2 = (p + 2) * p
Rearranging the equation, we get:
8 = p^2 + 2p
This is the quadratic equation that represents the given situation.
3. To find the solution from the quadratic equation, let's set it equal to zero:
p^2 + 2p - 8 = 0
We can solve this equation by factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula:
p = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 1, b = 2, and c = -8. Plugging these values into the quadratic formula, we have:
p = (-2 ± √(2^2 - 4(1)(-8))) / (2(1))
p = (-2 ± √(4 + 32)) / 2
p = (-2 ± √36) / 2
p = (-2 ± 6) / 2
Simplifying further, we get two possible solutions:
p1 = (-2 + 6) / 2 = 2
p2 = (-2 - 6) / 2 = -4
Since we are dealing with length and width, we discard the negative value as it doesn't make sense in this context.
Therefore, the width of the table, p, is 2 meters.
4. Finally, let's find the dimensions of the table:
Using the value of p we found, which is 2 meters, the width of the table is 2 meters.
The length of the table is obtained by adding 2 meters to the width:
Length = Width + 2
Length = 2 + 2
Length = 4 meters
Therefore, the table has a width of 2 meters and a length of 4 meters.