Mang jose wants to make a table which has an area of 6m, the length of the table has to be 1m longer than the width. If the width of the table is p meters, what will be the length. Form a quadratic equation that represent the equation.
width --- p
length -- p+1
p(p+1) = 6
p^2 + p - 6 = 0
easy to solve by factoring...
Width --- p
length --- p+1
p(p+1)=6
p^2 + p - 6 = 0
Without actually computing for the roots, determine whether the dimensions of the are rational numbers. Explain
To solve this problem, we need to form a quadratic equation that represents the given scenario. Let's start by understanding the information provided.
1. The area of the table is 6m².
2. The length of the table is 1m longer than the width.
3. The width of the table is p meters.
To find the length of the table, we can set up the equation based on the area formula, which is:
Area = Length × Width
Substituting the given values:
6m² = Length × Width
Since the length is 1m longer than the width, we can express the length as (p + 1) metres.
Now, we can substitute the length and width in the area equation:
6m² = (p + 1)m × p
Simplifying further, we get:
6m² = p² + p
This equation represents the situation where the area of the table is 6m², and the length is 1m longer than the width.
Therefore, the quadratic equation that represents the given scenario is:
p² + p - 6 = 0