Question

The length of a rectangular lot is 6 feet less than 3 times its

width. Its area is 222 square feet.
Its width is
feet and its length is
feet.

Answer 1

Length = 22.98 feet

Width = 9.66 feet

Explanation:

Let the length of the rectangle be L.

Let the width of the rectangle be W.

Given the following data;

Area of rectangle = 222 feet²

Translating the word problem into an algebraic expression, we have;

L = 3W - 6 ...... equation 1

We know that the area of a rectangle is given by the formula;

A = L * W

Substituting

222 = L * W ....equation 2

Substituting eqn 1 into eqn 2, we have;

222 = (3W - 6) * W

222 = 3W² - 6W

Rearranging the equation, we have;

3W² - 6W - 222 = 0

Next, we would use the quadratic formula to solve for the roots.

Note: the standard form of a quadratic equation is ax² + bx + c = 0

a = 3, b = -6 and c = -222

Solving the quadratic equation using the quadratic formula;

The quadratic equation formula is;

`x = \frac {-b \; \pm \sqrt {b^(2) - 4ac}}{2a}`

Substituting into the equation, we have;

`x = \frac {-(-6) \; \pm \sqrt {6^(2) - 4*3*(-222)}}{2*3}`

`x = \frac {6 \pm \sqrt {36 - (-2664)}}{6}`

`x = \frac {6 \pm \sqrt {36 + 2664}}{6}`

`x = \frac {6 \pm \sqrt {2700}}{6}`

`x = \frac {6 \pm 51.96}{6}`

`x_(1) = \frac {6 + 51.96}{6}`

`x_(1) = \frac {57.96}{6}`

x1 = 9.66

We do not need the negative value of x, so we proceed.

Therefore, Width, W = x1 = 9.66 feet

For the length;

L = 3W - 6

L = 3(9.66) - 6

L = 28.98 - 6

L = 22.98 feet