The sum of the length and breadth of a rectangle is 37 cm. The length is 11 cm more than the breadth. What is the breadth?
Answer and explanation
Correct answer: 13 cm
Let the length be l cm and the breadth be b cm. The sum condition gives l + b = 37, while the statement that the length exceeds the breadth by 11 gives l − b = 11. Subtract the second equation from the first: (l+b) − (l−b) = 37−11, so 2b = 26. Therefore b = 13 cm. The corresponding length is l = 13 + 11 = 24 cm, and 24 + 13 = 37 verifies the first condition. Thus option C is correct. The other proposed breadths would produce lengths 22, 23 or 25 cm from the difference condition, whose sums with the breadth are 33, 35 or 39 cm, not 37.
Frequently asked questions
What is the correct answer to this question?
13 cm
Why is this the correct answer?
Let the length be l cm and the breadth be b cm. The sum condition gives l + b = 37, while the statement that the length exceeds the breadth by 11 gives l − b = 11. Subtract the second equation from the first: (l+b) − (l−b) = 37−11, so 2b = 26. Therefore b = 13 cm. The corresponding length is l = 13 + 11 = 24 cm, and 24 + 13 = 37 verifies the first condition. Thus option C is correct. The other proposed breadths would produce lengths 22, 23 or 25 cm from the difference condition, whose sums with the breadth are 33, 35 or 39 cm, not 37.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Algebraic methods: Substitution method and Elimination method..
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