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
Ratio of perimeter of two similar triangles is equal to ratio of their corresponding sides
∴ (𝑷𝒆𝒓𝒊𝒎𝒆𝒕𝒆𝒓 Δ 𝑨𝑩𝑪)/(𝑷𝒆𝒓𝒊𝒎𝒆𝒕𝒆𝒓 Δ 𝑷𝑸𝑹)=𝑨𝑩/𝑷𝑸
We know that
Ratio of area of similar triangles is equal to square of ratio of its corresponding sides
(𝐴𝑟𝑒𝑎 𝑜𝑓" " ∆𝐴𝐵𝐶)/(𝐴𝑟𝑒𝑎 𝑜𝑓" " ∆𝑃𝑄𝑅)=(𝐴𝐵/𝑃𝑄)^2
(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)
Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.
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