A rectangle has area 150 cm². Its length is 5 cm more than its breadth. What is its length?
Answer and explanation
Correct answer: 15 cm
Use the rectangle area relationship, area = length × breadth. Let the breadth be x cm. Since the length is 5 cm greater, it is x + 5 cm. The given area produces x(x + 5) = 150, or x² + 5x − 150 = 0. Factoring gives (x + 15)(x − 10) = 0. The algebraic solutions are x = −15 and x = 10, but a physical breadth must be positive, so the breadth is 10 cm. Consequently, the length is x + 5 = 15 cm. Verification gives 10 × 15 = 150, so option C is correct. Option A is the breadth rather than the requested length; 12 and 20 do not form a pair whose product is 150 and whose difference is 5.
Frequently asked questions
What is the correct answer to this question?
15 cm
Why is this the correct answer?
Use the rectangle area relationship, area = length × breadth. Let the breadth be x cm. Since the length is 5 cm greater, it is x + 5 cm. The given area produces x(x + 5) = 150, or x² + 5x − 150 = 0. Factoring gives (x + 15)(x − 10) = 0. The algebraic solutions are x = −15 and x = 10, but a physical breadth must be positive, so the breadth is 10 cm. Consequently, the length is x + 5 = 15 cm. Verification gives 10 × 15 = 150, so option C is correct. Option A is the breadth rather than the requested length; 12 and 20 do not form a pair whose product is 150 and whose difference is 5.
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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