Let's assume the width of the rectangle is x mm.
According to the question, the length is 6 mm less than three times the width, which means the length is (3x - 6) mm.
We know that the area of a rectangle is calculated by multiplying the length and width, so we can write the equation:
Length * Width = Area
(3x - 6) * x = 105
Expanding the equation, we get:
3x^2 - 6x - 105 = 0
To solve this quadratic equation, we can either factor it or use the quadratic formula. Let's use the quadratic formula in this case:
x = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values from our equation:
a = 3, b = -6, c = -105
x = (-(-6) ± √((-6)^2 - 4 * 3 * -105)) / (2 * 3)
x = (6 ± √(36 + 1260)) / 6
x = (6 ± √1296) / 6
x = (6 ± 36) / 6
x = (6 + 36) / 6 or x = (6 - 36) / 6
x = 42 / 6 or x = -30 / 6
x = 7 or x = -5
Since the width cannot be negative, we discard the solution x = -5.
Therefore, the width of the rectangle is 7 mm.
To find the length, we substitute the value of x into the expression (3x - 6):
Length = 3x - 6 = 3 * 7 - 6 = 21 - 6 = 15 mm
Therefore, the dimensions of the rectangle are:
Width = 7 mm
Length = 15 mm
The area of a rectangle is 105mm^2 . The length is six millimeters less than three times its width. Find the dimensions of the rectangle
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