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 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.