Respuesta :
Answer:
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.
Answer:
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.
