Question

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?

Answer 1

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

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}* \text{Width}`

Putting the values, we get:

`x^2 - 12x + 32 = (x - 4) * \text{Width}\\\\\text{Width} = (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} = (x^2 - 12x + 32)/(x-4) = ((x-8)(x-4))/((x-4)) = x - 8`

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