Question
The length of a rectangle is seven less than twice the length of its width. If the area of the rectangle is 15 square meters, find the value of x.
Answers
GPT 3.5
Let's denote the width of the rectangle as 'w' and the length as '2w - 7'.
We know that the area of a rectangle is given by the formula: length x width
So we have the equation:
Area = length x width
15 = (2w - 7) x w
Expanding the right side of the equation, we get:
15 = 2w^2 - 7w
Rearranging the equation into a standard quadratic form, we get:
2w^2 - 7w - 15 = 0
Now we need to solve this quadratic equation to find the value of 'w'. We can either factor the equation or use the quadratic formula.
Factoring the equation gives us:
(2w + 3)(w - 5) = 0
This gives us two possible solutions: w = -3/2 or w = 5. Since the width cannot be negative, we take w = 5.
Substitute the value of 'w' back into '2w - 7' to find the length:
length = 2w - 7
length = 2(5) - 7
length = 10 - 7
length = 3
Therefore, the width of the rectangle is 5 meters and the length is 3 meters.
We know that the area of a rectangle is given by the formula: length x width
So we have the equation:
Area = length x width
15 = (2w - 7) x w
Expanding the right side of the equation, we get:
15 = 2w^2 - 7w
Rearranging the equation into a standard quadratic form, we get:
2w^2 - 7w - 15 = 0
Now we need to solve this quadratic equation to find the value of 'w'. We can either factor the equation or use the quadratic formula.
Factoring the equation gives us:
(2w + 3)(w - 5) = 0
This gives us two possible solutions: w = -3/2 or w = 5. Since the width cannot be negative, we take w = 5.
Substitute the value of 'w' back into '2w - 7' to find the length:
length = 2w - 7
length = 2(5) - 7
length = 10 - 7
length = 3
Therefore, the width of the rectangle is 5 meters and the length is 3 meters.