Mathematics: 9. The area of a yard is given by the equation y = x2 – 12x + 32. If the length of the garden is given by the expression x – 4, what is the width of the yard?

4(x -3)(x +3) = 0 has solutions x ∈ {-3, 3}....

9. The area of a yard is given by the equation y =

arwasoliman363

18.01.2022

The width of the yard is given by the expression (x - 8).

Step-by-step explanation:

We are given the following in the question:

Area of yard, y =

y = x^2 - 12x + 32

Length of garden =

x -4

We have to find the with of the garden.

Area of yard =

$\text{Length}\times \text{Width}$

Putting the values, we get:

$x^2 - 12x + 32 = (x - 4) \times \text{Width}\\\\\text{Width} = \dfrac{x^2 - 12x + 32}{x-4}$

Now,

$x^2 - 12x + 32 \\=x^2 - 8x - 4x + 32\\=x(x-8)-4(x-8)\\=(x-8)(x-4)$

$\text{Width} = \dfrac{x^2 - 12x + 32}{x-4} = \dfrac{(x-8)(x-4)}{(x-4)} = x - 8$

Thus, the width of the yard is given by the expression (x - 8).

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