A school has two rectangular playgrounds, which are similar in shape. If the length and the breadth of the first playground are given as 224 m and 160 m, respectively, then which of the following options CANNOT be the dimensions of the second playground?

Given:

A school has two rectangular playgrounds, which are similar in shape. If the length and the breadth of the first playground are given as 224 m and 160 m, respectively, then which of the following options CANNOT be the dimensions of the second playground?

Formula Used:

For similar rectangles, the ratio of the lengths should be equal to the ratio of the breadths.

Calculation:

Length = 224 m, Breadth = 160 m

Ratio = 224 / 160 = 7 / 5

Checking options:

Option 1: Length = 168 m; Breadth = 120 m

⇒ Ratio = 168 / 120 = 7 / 5 (Valid)

Option 2: Length = 343 m; Breadth = 255 m

⇒ Ratio = 343 / 255

⇒ 343 ÷ 7 = 49, 255 ÷ 5 = 51

⇒ Ratio ≠ 7 / 5 (Invalid)

Option 3: Length = 273 m; Breadth = 195 m

⇒ Ratio = 273 / 195

⇒ 273 ÷ 39 = 7, 195 ÷ 39 = 5

⇒ Ratio = 7 / 5 (Valid)

Option 4: Length = 210 m; Breadth = 150 m

⇒ Ratio = 210 / 150 = 7 / 5 (Valid)

∴ The correct answer is option 2.