Question

Completing the square: The length of the sides of a rectangular window have the ratio 1.6 to 1. The area of the window is 2822.4 in squared. What are the window dimensions?

Answer 1

To find the dimensions of the rectangular window, you can set up a ratio of length to width and solve for the variables. The width of the window is 40 inches and the length is 64 inches.

Step-by-step explanation:

To find the dimensions of the rectangular window, first, let's set up the ratio of length to width. We know that the ratio is 1.6 to 1. Let the width be 'x', then the length would be 1.6 times 'x'. The area of a rectangle is found by multiplying the length and width, so we can set up the equation:

(1.6x)(x) = 2822.4

Simplifying, we get:

1.6x^2 = 2822.4

Divide both sides by 1.6:

x^2 = 1764

Take the square root of both sides:

x = ±40

Since we are looking for the positive value of the width, the width of the window is 40 inches. The length can be found by multiplying the width by 1.6:

Length = 1.6 x 40 = 64 inches