Question
The length of a table is 4m longer than the width. The are is 60m^2. Find the dimensions of the table.
Answers
GPT 3.5
Let's assume that the width of the table is 'x' meters.
According to the given information, the length of the table is 4 meters longer than the width, so it would be 'x + 4' meters.
The area of the table is given by the product of length and width, which is '60m²'.
So, we have the equation:
Length * Width = Area
(x + 4) * x = 60
Expanding the equation:
x² + 4x = 60
Rearranging the equation:
x² + 4x - 60 = 0
Now we can solve this quadratic equation by factoring or using the quadratic formula.
Factoring, we get:
(x - 6)(x + 10) = 0
Setting each factor equal to zero:
x - 6 = 0 or x + 10 = 0
Solving each equation, we find:
x = 6 or x = -10
Since the width cannot be negative, we discard the solution 'x = -10'.
Therefore, the width of the table is 'x = 6' meters.
And the length of the table would be 'x + 4 = 6 + 4 = 10' meters.
So, the dimensions of the table are:
Width = 6 meters
Length = 10 meters
According to the given information, the length of the table is 4 meters longer than the width, so it would be 'x + 4' meters.
The area of the table is given by the product of length and width, which is '60m²'.
So, we have the equation:
Length * Width = Area
(x + 4) * x = 60
Expanding the equation:
x² + 4x = 60
Rearranging the equation:
x² + 4x - 60 = 0
Now we can solve this quadratic equation by factoring or using the quadratic formula.
Factoring, we get:
(x - 6)(x + 10) = 0
Setting each factor equal to zero:
x - 6 = 0 or x + 10 = 0
Solving each equation, we find:
x = 6 or x = -10
Since the width cannot be negative, we discard the solution 'x = -10'.
Therefore, the width of the table is 'x = 6' meters.
And the length of the table would be 'x + 4 = 6 + 4 = 10' meters.
So, the dimensions of the table are:
Width = 6 meters
Length = 10 meters