Quadratic Equations

3.5 completing the square by S. keel

The lengths of the sides of a rectangular window have the ratio 1.6 to 1. The area of the window is 2822.4 in^2. What are the window dimensions?

For this word problem, we will have to know what completing the square is and we will also need to know the formula for area. Completing the square is defined as the process of converting a quadratic equation into a perfect square trinomial by adding or subtracting terms on both sides. The formula for area is shown below.

I started by illustrating the length and width values for the window and substituting the values into the area formula. Then, I solved for x to find one of the lengths.

Since x=42, I plugged 42 into 1.6x to find the other side length.

Since x=42, and 1.6x=67.2, the dimensions of the window are 42 inches by 67.2 inches.

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