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
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ADRE 1.0 SLRC 2022 PAPER-III SOLVED QUESTIONS |
Solution
Given Ratios:
- The sides of the triangle are in the ratio
- The sides of the triangle are in the ratio
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:
- So, the ratios become
Express the Sides Using a Common Multiplier:
- Let the sides be , , and .
Using the Perimeter:
- The perimeter of the triangle is given as 104 cm.
- The perimeter is the sum of the sides:
- Simplify the equation:
Solve for :
Find the Lengths of the Sides:
- The sides are cm, cm, and cm.
Identify the Longest Side:
- The longest side is
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.
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