It is given that βˆ† ABC ~ βˆ† PQR, with BC/QR = 1/3. Then, (ar (PRQ))/(ar (BCA)) is equal to

(A) 9  (B) 3  (C) 1/3  (D) 1/9

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  1. Chapter 6 Class 10 Triangles (Term 1)
  2. Serial order wise

Transcript

Question 10 It is given that βˆ† ABC ~ βˆ† PQR, with BC/QR = 1/3. Then, (π‘Žπ‘Ÿ (𝑃𝑅𝑄))/(π‘Žπ‘Ÿ (𝐡𝐢𝐴)) is equal to (A) 9 (B) 3 (C) 1/3 (D) 1/9 We know that For similar triangles, ratio of Area of triangle is equal to the ratio of square of corresponding sides (π΄π‘Ÿπ‘’π‘Ž π‘œπ‘“ βˆ† 𝐴𝐡𝐢)/(π΄π‘Ÿπ‘’π‘Ž π‘œπ‘“ βˆ† 𝑃𝑄𝑅)=(𝐡𝐢)^2/(𝑄𝑅)2 (π΄π‘Ÿπ‘’π‘Ž π‘œπ‘“ βˆ† 𝐴𝐡𝐢)/(π΄π‘Ÿπ‘’π‘Ž π‘œπ‘“ βˆ† 𝑃𝑄𝑅)=(𝐡𝐢/𝑄𝑅)^2 (π΄π‘Ÿπ‘’π‘Ž π‘œπ‘“ βˆ† 𝐴𝐡𝐢)/(π΄π‘Ÿπ‘’π‘Ž π‘œπ‘“ βˆ† 𝑃𝑄𝑅)=(1/3)^2 (π΄π‘Ÿπ‘’π‘Ž π‘œπ‘“ βˆ† 𝐴𝐡𝐢)/(π΄π‘Ÿπ‘’π‘Ž π‘œπ‘“ βˆ† 𝑃𝑄𝑅)=1/9 But, we need to find ratio (π‘Žπ‘Ÿ (𝑃𝑅𝑄))/(π‘Žπ‘Ÿ (𝐡𝐢𝐴)) (𝒂𝒓 (𝑷𝑹𝑸))/(𝒂𝒓 (𝑩π‘ͺ𝑨)) = 9 So, the correct answer is (A)

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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.