The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is

(A) 5   (B) 12  (C) 11   (D) 7 + √5

 

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  1. Chapter 7 Class 10 Coordinate Geometry (Term 1)
  2. Serial order wise

Transcript

Question 9 The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is (A) 5 (B) 12 (C) 11 (D) 7 + โˆš5 Let A (0, 4), B (0, 0) and C (3, 0) Thus, Perimeter of triangle = AB + BC + AC Finding AB AB = โˆš((๐‘ฅ2 โˆ’๐‘ฅ1)2+(๐‘ฆ2 โˆ’๐‘ฆ1)2) = โˆš(( 0โˆ’0)2+(0 โˆ’4)2) = โˆš(02+(โˆ’4)2) = โˆš16 = โˆš(4^2 ) = 4 units Finding AC Here, A (0, 4) and C (3, 0) AC = โˆš((๐‘ฅ2 โˆ’๐‘ฅ1)2+(๐‘ฆ2 โˆ’๐‘ฆ1)2) = โˆš((3โˆ’0)2+(0 โˆ’4)2) = โˆš(32+(โˆ’4)2) = โˆš(9+ 16) = โˆš25 = โˆš(5^2 ) = 5 units Finding BC Here, B (0, 0) and C (3, 0) BC = โˆš((๐‘ฅ2 โˆ’๐‘ฅ1)2+(๐‘ฆ2 โˆ’๐‘ฆ1)2) = โˆš((3โˆ’0)2+(0 โˆ’0)2) = โˆš(32+(0)2) = โˆš(9+0) = โˆš9 = โˆš(3^2 ) = 3 units Thus, AB = 4, AC = 5, BC = 3 Therefore, Perimeter of triangle = AB + BC + AC = 4 + 3 + 5 = 12 units So, the correct answer is (B)

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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.