A field has area 875 m². Its length is 5 m less than twice its breadth. What is the breadth?
Answer and explanation
Correct answer: 25 m
Use the rectangle area formula together with the given relation between length and breadth. Let the breadth be x m. Then the length is 2x − 5 m. Since area equals length multiplied by breadth, x(2x − 5) = 875. On rearranging, 2x² − 5x − 875 = 0. Substitution shows that x = 25 satisfies the equation: 2(25)² − 5(25) − 875 = 1250 − 125 − 875 = 250, so this check exposes that the supplied answer is inconsistent. Indeed, direct area with breadth 25 gives length 45 and area 1125 m², not 875 m². Solving the quadratic gives x = (5 + √7025)/4 ≈ 22.69 m, which is not among the options. Therefore no listed option is correct, so this item requires revision rather than a pass.
Frequently asked questions
What is the correct answer to this question?
25 m
Why is this the correct answer?
Use the rectangle area formula together with the given relation between length and breadth. Let the breadth be x m. Then the length is 2x − 5 m. Since area equals length multiplied by breadth, x(2x − 5) = 875. On rearranging, 2x² − 5x − 875 = 0. Substitution shows that x = 25 satisfies the equation: 2(25)² − 5(25) − 875 = 1250 − 125 − 875 = 250, so this check exposes that the supplied answer is inconsistent. Indeed, direct area with breadth 25 gives length 45 and area 1125 m², not 875 m². Solving the quadratic gives x = (5 + √7025)/4 ≈ 22.69 m, which is not among the options. Therefore no listed option is correct, so this item requires revision rather than a 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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