Question

An architect is designing square windows with an area of (x^2+20x+100) ft^2. The dimensions of the windows are of the form a X plus B where a and b are whole numbers

A. Find the dimensions of each square window

Answer 1

The dimensions of the window are (x + 10) and (x + 10).

To get this answer, we have to look for 2 numbers that when multiplied together give us the given polynomial. We know the form of the numbers, they are x + a and x + b.

If you multiply (x + 10) times (x + 10), you get the polynomial x^2 + 20x + 100.

Answer 2

The expression that represents the width and length of the square is (x+10).

We factor this expression to find the dimensions. We want factors of 100 that sum to 20; 10(10) = 100 and 10+10=20. This gives us

(x+10)(x+10).