The length of a rectangle is seven less than twice the length of its width if the area of the rectangle is 15 m² find the value of X.
Let the width of the rectangle be x.
Then, the length of the rectangle is 2x - 7.
The area of the rectangle is given by the formula:
Area = length x width
Therefore, we have:
15 = (2x - 7) * x
15 = 2x^2 - 7x
2x^2 - 7x - 15 = 0
Now, we can solve this quadratic equation using either factoring, completing the square, or the quadratic formula. Let's use factoring:
2x^2 - 10x + 3x - 15 = 0
2x(x - 5) + 3(x - 5) = 0
(2x + 3)(x - 5) = 0
Setting each factor to zero, we get:
2x + 3 = 0 or x - 5 = 0
x = -3/2 or x = 5
Since the width cannot be negative, the only valid solution is:
x = 5
Therefore, the value of x is 5.