The width of a rectangle is 3 units less than the length. If the area is 70 square units, then find the dimensions of the rectangle.
To find the dimensions of the rectangle, we can start by representing the length of the rectangle as 'x'. Since the width is 3 units less than the length, we can represent the width as 'x - 3'.
We know that the area of a rectangle is given by the formula:
Area = Length * Width
Given that the area is 70 square units, we can set up the equation:
70 = x * (x - 3)
To solve this equation, we can simplify it:
70 = x^2 - 3x
Next, we bring all the terms to one side of the equation to set it equal to zero:
x^2 - 3x - 70 = 0
Now, we can factor this quadratic equation or use the quadratic formula to solve for 'x'. Factoring this particular equation would be a bit tricky, so let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
In our equation, a = 1, b = -3, and c = -70. Substituting these values into the quadratic formula, we have:
x = (-(-3) ± √((-3)^2 - 4(1)(-70))) / (2 * 1)
Simplifying further:
x = (3 ± √(9 + 280)) / 2
x = (3 ± √289) / 2
x = (3 ± 17) / 2
This gives us two possible values for 'x':
x = (3 + 17) / 2 or x = (3 - 17) / 2
x = 20 / 2 or x = -14 / 2
x = 10 or x = -7
Since a length cannot be negative, we exclude x = -7 from our solution.
Therefore, the length of the rectangle is x = 10 units.
To find the width, we substitute this value back into the expression 'x - 3':
Width = x - 3 = 10 - 3 = 7 units
So, the dimensions of the rectangle are length = 10 units and width = 7 units.
L(L-3)=70
Hmmm. 10*7 = 70