Question

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 statements 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.

Answer 1

The statement that is true for the retangular doors and windows is the area of the door is 3.24 times the area of the window.

Perimeter of a rectangle

The perimeter of a rectangle is the sum of the whole side of the rectangle.

Therefore,

perimeter of a rectangle = 2l + 2w

where

• l = length
• w = width

Therefore, each dimension of the door is 1.8 times the dimension of the window.

Hence,

let

the width of the window = x

the length of the window = y

Therefore,

perimeter = 2(x+ y)

The perimeter of the doors will be as follows:

perimeter of the doors = 2(1.8(x) + 1.8(y))

perimeter of the doors = 3.6(x + y)

Area of rectangle

area = lw

Therefore,

area of window = xy

area of doors = 1.8x(1.8y)

area of doors =  3.24xy

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