The length of a rectangle is 11ft less than three times the width, and the area of the rectangle is 42ft^2. Find the dimensions of the rectangle

Answer 1

Let the width of the rectangle be represented by x ft.

Therefore, the length of the rectangle is 3x - 11 ft.

The area of a rectangle is given by the formula: Area = length * width

Given that the area is 42 ft^2, we can set up the equation:

x(3x - 11) = 42

Expanding and simplifying the equation:

3x^2 - 11x = 42

Rearranging the equation into standard form:

3x^2 - 11x - 42 = 0

We will then factorize the quadratic equation:

(3x + 7)(x - 6) = 0

Setting each factor to zero:

3x + 7 = 0 or x - 6 = 0

3x = -7 or x = 6

x = -7/3 is not a valid solution for the width, so the valid width is x = 6 ft.

Therefore, the width of the rectangle is 6 ft and the length is 3(6) - 11 = 18 - 11 = 7 ft.

So, the dimensions of the rectangle are width = 6 ft and length = 7 ft.