an architect designs a rectangular window such that the width of the window is 40 com less than the height. If the perimeter of the window is 500 cm, what are the widths and heights?

2(w + w+40) = 500

2 h + 2 w = 400

h + w = 200

w + 40 + w = 200

2 w = 160

w = 80

h = 120

I used 400, use 500

To solve this problem, let's assume the height of the window is h cm. According to the problem, the width of the window is 40 cm less than the height, so the width would be (h - 40) cm.

The perimeter of a rectangular window is calculated by adding the lengths of all four sides. In this case, we have two widths and two heights, so the perimeter can be expressed as:

Perimeter = 2 * Width + 2 * Height

Now, we can plug in the values:

500 cm = 2 * (h - 40) cm + 2 * h cm

Simplify the equation:

500 cm = 2h - 80 cm + 2h cm

Combine like terms:

500 cm = 4h - 80 cm

Now, isolate the variable on one side of the equation:

4h = 580 cm

Divide both sides of the equation by 4:

h = 145 cm

Now that we have the height, we can substitute it back into the expression for the width:

Width = h - 40 cm = 145 cm - 40 cm = 105 cm

So, the height of the window is 145 cm and the width is 105 cm.