## The perimeters of two similar triangles ∆ABC and ∆PQR are 35 cm & 45 cm respectively, then the ratio of the areas of the two triangles is______________

Last updated at Nov. 1, 2019 by Teachoo

Transcript

Question 13 The perimeters of two similar triangles ∆ABC and ∆PQR are 35 cm & 45 cm respectively, then the ratio of the areas of the two triangles is______________ Since ΔABC and ΔPQR are similar, the ratio of their corresponding sides is same 𝐴𝐵/𝑃𝑄=𝐵𝐶/𝑄𝑅=𝐴𝐶/𝑃𝑅 Let 𝐴𝐵/𝑃𝑄=𝐵𝐶/𝑄𝑅=𝐴𝐶/𝑃𝑅=𝑘 ∴ AB = kPQ BC = kQR AC = kPR Now, Perimeter of Δ ABC = AB + BC + AC = kPQ + kQR + kPR = k (PQ + QR + PR) = k × Perimeter of Δ PQR Therefore, (𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 𝑜𝑓" " ∆𝐴𝐵𝐶)/(𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 𝑜𝑓" " ∆𝑃𝑄𝑅) = k So, we can write 𝐴𝐵/𝑃𝑄=𝐵𝐶/𝑄𝑅=𝐴𝐶/𝑃𝑅=(𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 𝑜𝑓" " ∆𝐴𝐵𝐶)/(𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 𝑜𝑓" " ∆𝑃𝑄𝑅) " = k " 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 (𝐴𝑟𝑒𝑎 𝑜𝑓" " ∆𝐴𝐵𝐶)/(𝐴𝑟𝑒𝑎 𝑜𝑓" " ∆𝑃𝑄𝑅)=((𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 𝑜𝑓" " ∆𝐴𝐵𝐶)/(𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 𝑜𝑓" " ∆𝑃𝑄𝑅))^2 Putting values (𝐴𝑟𝑒𝑎 𝑜𝑓" " ∆𝐴𝐵𝐶)/(𝐴𝑟𝑒𝑎 𝑜𝑓" " ∆𝑃𝑄𝑅)=(35/45)^2 (𝐴𝑟𝑒𝑎 𝑜𝑓" " ∆𝐴𝐵𝐶)/(𝐴𝑟𝑒𝑎 𝑜𝑓" " ∆𝑃𝑄𝑅)=(7/9)^2 (𝐴𝑟𝑒𝑎 𝑜𝑓" " ∆𝐴𝐵𝐶)/(𝐴𝑟𝑒𝑎 𝑜𝑓" " ∆𝑃𝑄𝑅)=49/81 Hence, the required ratio is 49:81

CBSE Class 10 Sample Paper for 2020 Boards - Maths Standard

Paper Summary

Question 1 Important

Question 2 Important

Question 3

Question 4 Important

Question 5 Important

Question 6 Important

Question 7

Question 8 Important

Question 9 Important

Question 10

Question 11

Question 12 (OR 1st question)

Question 12 (OR 2nd question)

Question 13 Important You are here

Question 14 Important

Question 15 Important

Question 16

Question 17 Important

Question 18 (OR 1st question) Important

Question 18 (OR 2nd question) Important

Question 19

Question 20

Question 21 Important

Question 22 Important

Question 23 (OR 1st question) Important

Question 23 (OR 2nd question)

Question 24 Important

Question 25 (OR 1st question) Important

Question 25 (OR 2nd question)

Question 26 Important

Question 27 (OR 1st question)

Question 27 (OR 2nd question) Important

Question 28 Important

Question 29 (OR 1st question)

Question 29 (OR 2nd question)

Question 30 Important

Question 31 Important

Question 32 (OR 1st question) Important

Question 32 (OR 2nd question) Important

Question 33 Important

Question 34 Important

Question 35 (OR 1st question) Important

Question 35 (OR 2nd question)

Question 36

Question 37 (OR 1st question)

Question 37 (OR 2nd question)

Question 38 (OR 1st question)

Question 38 (OR 2nd question) Important

Question 39

Question 40 Important

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.