When both length and breadth of a rectangle are increased by 6 cm, the area increases by 480 square cm. If the original length is 12 cm more than the breadth, what is the breadth?
Answer and explanation
Correct answer: 31 cm
Let the original breadth be x cm. Then the original length is x + 12 cm. The original area is x(x + 12), and after increasing both dimensions by 6 cm, the new area is (x + 6)(x + 18). Their difference is 480: (x + 6)(x + 18) − x(x + 12) = 480. Expanding gives x² + 24x + 108 − x² − 12x = 480, so 12x + 108 = 480 and x = 31. Thus the breadth is 31 cm, option B. Substitution confirms the increase: 37×24 − 31×43 = 888 − 1333? The dimensions must be ordered correctly: new length 49 and new breadth 37, giving 1813 − 1333 = 480.
Frequently asked questions
What is the correct answer to this question?
31 cm
Why is this the correct answer?
Let the original breadth be x cm. Then the original length is x + 12 cm. The original area is x(x + 12), and after increasing both dimensions by 6 cm, the new area is (x + 6)(x + 18). Their difference is 480: (x + 6)(x + 18) − x(x + 12) = 480. Expanding gives x² + 24x + 108 − x² − 12x = 480, so 12x + 108 = 480 and x = 31. Thus the breadth is 31 cm, option B. Substitution confirms the increase: 37×24 − 31×43 = 888 − 1333? The dimensions must be ordered correctly: new length 49 and new breadth 37, giving 1813 − 1333 = 480.
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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