When both the length and breadth of a rectangle are increased by 4 cm, its area increases by 224 square cm. If the original length is 10 cm more than the breadth, what is the original breadth?
Answer and explanation
Correct answer: 20 cm
Let the original breadth be x cm. The original length is then x + 10 cm. After increasing both dimensions by 4 cm, the new dimensions are x + 4 and x + 14. The increase in area is therefore (x + 4)(x + 14) − x(x + 10) = 224. Expanding gives x² + 18x + 56 − x² − 10x = 224, so 8x + 56 = 224 and 8x = 168. Hence x = 21, not 20. Therefore the supplied correct option and answer choices are inconsistent: none of A–D is correct. The mathematically correct breadth is 21 cm, so this item requires revision before it can pass.
Frequently asked questions
What is the correct answer to this question?
20 cm
Why is this the correct answer?
Let the original breadth be x cm. The original length is then x + 10 cm. After increasing both dimensions by 4 cm, the new dimensions are x + 4 and x + 14. The increase in area is therefore (x + 4)(x + 14) − x(x + 10) = 224. Expanding gives x² + 18x + 56 − x² − 10x = 224, so 8x + 56 = 224 and 8x = 168. Hence x = 21, not 20. Therefore the supplied correct option and answer choices are inconsistent: none of A–D is correct. The mathematically correct breadth is 21 cm, so this item requires revision before it can pass.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Word Problems and Applications.
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