Directions – : The following questions are accompanied by three statement A, B and C. you have to determine which statement (s) is /are necessary/ sufficient to answer the question.
Find the area of a rhombus. A. Sum of the squares
of the diagonals is 256 m². B. Perimeter of the rhombus is 32 m. C. Ratio of one diagonal and the side is 3:8
AOnly A and B togetherCorrect AnswerIncorrect Answer
BOnly CCorrect AnswerIncorrect Answer
CC and either A or BCorrect AnswerIncorrect Answer
DAny two of themCorrect AnswerIncorrect Answer
EAll statements are requiredCorrect AnswerIncorrect Answer
Solution
If d₁ and d₂ be the diagonals and a the length of the side of the rhombus then From 1: d₁²+ d₂² = 4a² = 256 a² = 64 a = 8 From 2:
Perimeter = 4a
32 = 4a a = 8 From 3: d₁ : a = 3 : 8 Therefore, by combining C and either A or B, a = 8,d₁ = 3 so we can find d₂ by using, d₁²+ d₂² = 4a² then we can find area of rhombus = 1/2 * d1* d2Hence by combining C and either A or B are required to answer as A & B are same.