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Lemur [1.5K]
3 years ago
15

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 o

f 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
Mathematics
1 answer:
Basile [38]3 years ago
6 0

Answer:

Length = 16 or -5 feet.

Width = 5 or -16 feet.

Step-by-step explanation:

Let the length of the concrete pad = l

Let the width of the concrete pad = w

<u>Given the following data;</u>

Area of concrete pad, a = 80ft²

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

l = 11 + w

<em>We know that, the area of rectangle, A = length * width</em>

A = l*w

<em>Substituting the values into the equation, we have;</em>

80 = (11 + w)w

<em>Expanding the bracket, we have;</em>

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.

<em>Therefore, the width of the concrete pad is 5 feet or -16 feet.</em>

<em>To find its length, l;</em>

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.

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