Can you draw a rectangle in your notebook whose width and height are proportional to the ratio of the blackboard?

Question

Homi · Accepted Answer

We will find the dimensions of a new rectangle that has the same width-to-height relationship as the blackboard.

Step 1 — Understand the blackboard's ratio

The question tells us the blackboard's width and height are proportional. The ratio of the blackboard's width to its height is given as 2:1. This means that for every 2 units of width, there is 1 unit of height.

Let $W_B$ be the blackboard's width. Let $H_B$ be the blackboard's height. The ratio can be written as: $\frac{W_B}{H_B} = \frac{2}{1}$ This equation shows that the blackboard's width is always twice its height. $W_B = 2 \times H_B$ We need to use this same relationship for our notebook rectangle.

Diagram 1

Step 2 — Choose dimensions for the notebook rectangle

We want to draw a rectangle in our notebook. Let $W_N$ be the notebook rectangle's width. Let $H_N$ be the notebook rectangle's height. For our notebook rectangle to be proportional to the blackboard, its width-to-height ratio must also be 2:1. So, we need: $\frac{W_N}{H_N} = \frac{2}{1}$ This means the notebook rectangle's width must be twice its height. $W_N = 2 \times H_N$ We can choose any suitable height for our notebook rectangle. Let us choose 5 cm. $H_N = 5 \text{ cm}$ Now, we calculate the width using the relationship $W_N = 2 \times H_N$ : $W_N = 2 \times 5 \text{ cm}$

$\boxed{W_N = 10 \text{ cm}}$ So, we can draw a rectangle with a width of 10 cm and a height of 5 cm. Let us check the ratio of these dimensions: $\frac{\text{Width}}{\text{Height}} = \frac{10 \text{ cm}}{5 \text{ cm}}$ $= \frac{2}{1}$ This ratio is 2:1, which is the same as the blackboard.

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I can draw a rectangle in my notebook whose width and height are proportional to the ratio of the blackboard. For example, I can draw a rectangle with: Width = 10 cm Height = 5 cm

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