Question

A carpenter is making a rectangular form for a concrete pad she wants the length of the path to be 11 feet more than the width of the bed the area of the concrete pad must be 80 ft.² write the quadratic equation that will be used to find the dimensions of the pad

Answer 1

Length = 16 or -5 feet.

Width = 5 or -16 feet.

Explanation:

Let the length of the concrete pad = l

Let the width of the concrete pad = w

Given the following data;

Area of concrete pad, a = 80ft²

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

`l = 11 + w`

We know that, the area of rectangle, A = length * width

`A = l*w`

Substituting the values into the equation, we have;

`80 = (11 + w)w`

Expanding the bracket, we have;

`80 = 11w + w^(2)`

`w^(2) + 11w - 80 = 0`

*Solving the quadratic equation by using factorization method*

`w^(2) + 16w - 5w - 80 = 0`

`w(w + 16) - 5(w + 16) = 0`

`(w - 5)(w + 16) = 0`

Width, w = 5 feet or w = -16 feet.

Therefore, the width of the concrete pad is 5 feet or -16 feet.

To find its length, l;

`l = 11 + w`

When w = 5 feet

`l = 11 + 5`

Length, l = 16 feet

When w = - 16 feet

`l = 11 + (-16)`

`l = 11 - 16`

Length, l = -5 feet.

Hence, the dimensions of the concrete pad is 16 by 5 feet or -5 by -16 feet.