Question

An architect is designing square windows with an area of(x2 + 16x +64) ft?. The dimensions of the

windows are of the form ax +b, where a and b are whole numbers.
Part 1 out of 2
Find an expression for the perimeter of the windows.
The perimeter of the square is represented by
(x+
6 ft.

Answer 1

A) The dimensions are (x+10) by (x+10).

B) The perimeter is given by 4x+40.

C) The perimeter when x is 4 is 56.

Explanation:

I filled two notebook papers to solve this

Answer 2

A) The dimensions are (x+10) by (x+10).

B) The perimeter is given by 4x+40.

C) The perimeter when x is 4 is 56.

The quadratic can be factored by finding factors of c, the constant, that sum to b, the coefficient of x. Our c is 100 and our b is 20; we want factors of 100 that sum to 20. 10*10=100 and 10+10=20, so those are what we need. This gives us (x+10)(x+10 for the factored form.

Since the dimensions are all (x+10), and there are 4 sides, the perimeter is given by 4(x+10). Using the distributive property we have 4*x+4*10=4x+40.

To find the perimeter when x=4, substitute 4 into our perimeter expression:

4*4+40=16+40=56.