Question

An architect is designing square windows with an area of ( x 2 + 20x + 100) ft2 . The dimensions of the windows are of the form ax + b, where a and b are whole numbers.

a. Find the dimensions of each square window.
b. Find an expression for the perimeter of a window.
c. Find the perimeter of a window when x = 4.

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.

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.