Compare the rectangle you have drawn to those drawn by your classmates. Do they all look the same?

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Homi · Accepted Answer

Rectangles with the same side ratio look alike, even if their sizes differ.

Step 1 — Understanding the Rectangle's Ratio

We drew a rectangle with a 2:1 length-to-width ratio. This means the length is always twice the width. Let $L$ be the length of the rectangle. Let $W$ be the width of the rectangle. The ratio of length to width is $L:W$ . We are given this ratio as $2:1$ . So, we can write this as a fraction.

$\frac{L}{W} = \frac{2}{1}$

This means that $L = 2 \times W$ . For example, if we choose a width of $4 \text{ cm}$ . Then the length would be $2 \times 4 \text{ cm}$ .

$L = 2 \times 4 \text{ cm}$

$\boxed{L = 8 \text{ cm}}$

So, one rectangle could be $8 \text{ cm}$ long and $4 \text{ cm}$ wide.

Diagram 1

Step 2 — Comparing Rectangles with the Same Ratio

Now, let us think about our classmates' drawings. They also followed the 2:1 length-to-width ratio. However, they might have chosen different widths. Let us look at some examples of rectangles they might have drawn. If a classmate chose a width of $3 \text{ cm}$ . Their length would be $2 \times 3 \text{ cm}$ .

$L = 2 \times 3 \text{ cm}$

$\boxed{L = 6 \text{ cm}}$

So, they drew a $6 \text{ cm} \times 3 \text{ cm}$ rectangle. Another classmate might have chosen a width of $6 \text{ cm}$ . Their length would be $2 \times 6 \text{ cm}$ .

$L = 2 \times 6 \text{ cm}$

$\boxed{L = 12 \text{ cm}}$

They drew a $12 \text{ cm} \times 6 \text{ cm}$ rectangle. All these rectangles have different actual sizes. However, their proportions are exactly the same. The length is always twice the width. This means their overall shape is identical. Only the scale, or how big they are, is different.

Answer

(i) Some classmates may draw a rectangle that is 8 cm long and 4 cm wide. (ii) Some classmates may draw a rectangle that is 6 cm long and 3 cm wide. (iii) Some classmates may draw a rectangle that is 12 cm long and 6 cm wide. (iv) Even though the sizes are different, the shape of all these rectangles is the same because they all follow the 2:1 proportional ratio. (v) Yes, all rectangles drawn with the same ratio (2:1) will look the same in shape, even if their sizes are different. Only the scale changes, not the shape.

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