Question

a wall contains a rectangular window. the area (in square feet) of the window is represented by x^2-4x+3. write a bionominal that represents the height of the window. find the permiteter when the wall is 10 feet. the square on the inside is (x-3) ft

Answer 1

The height of the wall would be x - 1 and the perimeter of the wall is 32 feet

How to determine the height?

The area of the window is given as:

A = x^2 - 4x + 3

Expand

A = x^2 - 3x - x + 3

Factorize

A = x(x - 3) - 1(x - 3)

Factor out x - 3

A = (x - 1)(x - 3)

The width of the wall is given as: x - 3

So, the height of the wall would be x - 1

How to determine the perimeter?

The perimeter is calculated using:

P = 2 *(Width + Height)

This gives

P = 2 * (x - 1 + x - 3)

When x = 10, we have:

P = 2 * (10 - 1 + 10 - 3)

Evaluate

P = 32

Hence, the perimeter of the wall is 32 feet

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