The ratio of the sides of a triangle is 1/2 : 1/3 : 1/4 and its perimeter is 104 cm. The longest arm of the triangle is || ADRE 1.0 SLRC 2022 PAPER-III SOLVED QUESTIONS

Question

The ratio of the sides of a triangle is 1/2 : 1/3 : 1/4 and its perimeter is 104 cm. The longest arm of the triangle is: 

    (A) 52 cm 

    (B) 48 cm 

    (C) 44 cm 

    (D) 40 cm

ADRE 1.0 SLRC 2022 PAPER-III SOLVED QUESTIONS


Solution

  1. Given Ratios:

    • The sides of the triangle are in the ratio 12:13:14\frac{1}{2} : \frac{1}{3} : \frac{1}{4}
  2. Finding a Common Multiplier:

    • To simplify the ratio, find a common denominator for the fractions. The least common multiple (LCM) of 2, 3, and 4 is 12.
    • Convert the fractions to have the same denominator:
      • 12=612\frac{1}{2} = \frac{6}{12}
      • 13=412\frac{1}{3} = \frac{4}{12}
      • 14=312\frac{1}{4} = \frac{3}{12}
    • So, the ratios become 6:4:36 : 4 : 3
  3. Express the Sides Using a Common Multiplier:

    • Let the sides be 6x6x, 4x4x, and 3x3x.
  4. Using the Perimeter:

    • The perimeter of the triangle is given as 104 cm.
    • The perimeter is the sum of the sides: 6x+4x+3x=104
    • Simplify the equation: 13x=10413x = 104
  5. Solve for xx:

    • x=10413x = \frac{104}{13}
    • x=8x = 8
  6. Find the Lengths of the Sides:

    • The sides are 6x=6×8=486x = 6 \times 8 = 48 cm, 4x=4×8=324x = 4 \times 8 = 32 cm, and 3x=3×8=243x = 3 \times 8 = 24 cm.
  7. Identify the Longest Side:

    • The longest side is 48cm.

So, the longest arm of the triangle is 48 cm


Importance for ADRE 2.0 

  • This type of question is important for ADRE 2.0 as it tests your understanding of ratios and their application in geometry. 
  • These skills are crucial for solving a wide range of mathematical problems in competitive exams. T
  • his specific question has been previously asked in ADRE 1.0 SLRC-2022 Paper III for Grade-III Posts, making it relevant for future exam preparation.

Comments