The perimeters of two similar triangles are 26 cm and 39 cm. The ratio of their areas will be

(a) 2 : 3   (b) 6 : 9   (c) 4 : 6   (d) 4 : 9

This question is inspired from Question 13 - Sample Papers 2020 - Maths Standard - [Also, check proof of the formula]

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  1. Class 10
  2. Solutions of Sample Papers for Class 10 Boards

Transcript

Question 33 The perimeters of two similar triangles are 26 cm and 39 cm. The ratio of their areas will be (a) 2 : 3 (b) 6 : 9 (c) 4 : 6 (d) 4 : 9 Let ΔABC and ΔPQR be two similar triangles Now, Ratio of perimeter of two similar triangles is equal to ratio of their corresponding sides ∴ (𝑷𝒆𝒓𝒊𝒎𝒆𝒕𝒆𝒓 Δ 𝑨𝑩𝑪)/(𝑷𝒆𝒓𝒊𝒎𝒆𝒕𝒆𝒓 Δ 𝑷𝑸𝑹)=𝑨𝑩/𝑷𝑸 26/39=𝐴𝐵/𝑃𝑄 2/3=𝐴𝐵/𝑃𝑄 𝑨𝑩/𝑷𝑸=𝟐/𝟑 We know that Ratio of area of similar triangles is equal to square of ratio of its corresponding sides Therefore, (𝐴𝑟𝑒𝑎 𝑜𝑓" " ∆𝐴𝐵𝐶)/(𝐴𝑟𝑒𝑎 𝑜𝑓" " ∆𝑃𝑄𝑅)=(𝐴𝐵/𝑃𝑄)^2 Putting values (𝐴𝑟𝑒𝑎 𝑜𝑓" " ∆𝐴𝐵𝐶)/(𝐴𝑟𝑒𝑎 𝑜𝑓" " ∆𝑃𝑄𝑅)=(2/3)^2 (𝑨𝒓𝒆𝒂 𝒐𝒇" " ∆𝑨𝑩𝑪)/(𝑨𝒓𝒆𝒂 𝒐𝒇" " ∆𝑷𝑸𝑹)=𝟒/𝟗 Hence, the required ratio is 4 : 9 So, the correct answer is (d)

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.