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

(A) 9Β  (B) 3Β  (C) 1/3Β  (D) 1/9

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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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.