Mario's house has a rectangular door and a rectangular window that are similar shapes. Each dimension of the door is 1.8 times the dimensions of the window. Which of the following is true?

A. The area of the door is 1.8 times the area of the window.

B. The area of the door is 3.6 times the area of the window.

C. The area of the door is 3.24 times the area of the window.

D. The perimeter of the door is 3.24 times the perimeter of the window

The area of the door is 3.24 times the area of the window.

Step-by-step explanation:

The area of a recangle is given by the following formula:

area = width*length

While the perimeter is given by:

perimeter = 2*width + 2*length

Assumint the width of the window is x and the length of the window is y, it's area and perimeter are:

window area = x*y

window perimeter = 2*x + 2*y

Since each dimension of the door is 1.8 times the dimensions of the window, then the door width = 1.8x and the door length = 1.8y. So the area and the perimeter are:

door area = (1.8*x) * (1.8*y) = 3.24*x*y

door perimeter = 2 * (1.8*x) + 2 * (1.8*y) = 3.6*x + 3.6*y = 3.6 * (x + y)

Since window area = x*y and window perimeter = (x + y), we have:

door area = 3.24 * (window area)

door perimeter = 3.6 * (window perimeter)

Therefore the correct answer is C. The area of the door is 3.24 times the area of the window.

C. The area of the door is 3.24 times the area of the window.

Step-by-step explanation:

Area of rectangle = length * width

Perimeter of a rectangle = 2 (length * width)

Let the dimension of the window be;

length = l

width = w

Area of window = l * w

= lw

Perimeter or window = 2 (l + w)

Given that: the dimension of the door is 1.8 times that of the window, dimension of door are;

length of door = 1.8l

width of door = 1.8w

Area of the door = 1.8l * 1.8 w

= 3.24lw

But area of window = lw, therefore;

∴ Area of door = 3.24 * Area of window

Perimeter of door = 2 (1.8l + 1.8w)

= 3.6 (l + w)

∴ Perimeter of door = 3.6 * Perimeter of window

Therefore, area of the door is 3.24 times the area of the window is the correct option.