The length of a rectangular field is 2 m less than three times its breadth. Its area is 161 m². What is the breadth?
Answer and explanation
Correct answer: 7 m
The governing idea is to translate the length condition and area formula into a quadratic equation. Let the breadth be x m. The length is three times the breadth minus 2, so it is 3x − 2 m. Using area = length × breadth gives x(3x − 2) = 161. Hence 3x² − 2x − 161 = 0. Testing the listed positive values, x = 7 gives 3(49) − 14 − 161 = 147 − 14 − 161 = 0. Algebraically, the equation factors as (x − 7)(3x + 23) = 0, producing x = 7 or x = −23/3. A breadth cannot be negative, so x = 7 m. Thus option B is correct, while the other options fail to produce the stated area with length 3x − 2.
Frequently asked questions
What is the correct answer to this question?
7 m
Why is this the correct answer?
The governing idea is to translate the length condition and area formula into a quadratic equation. Let the breadth be x m. The length is three times the breadth minus 2, so it is 3x − 2 m. Using area = length × breadth gives x(3x − 2) = 161. Hence 3x² − 2x − 161 = 0. Testing the listed positive values, x = 7 gives 3(49) − 14 − 161 = 147 − 14 − 161 = 0. Algebraically, the equation factors as (x − 7)(3x + 23) = 0, producing x = 7 or x = −23/3. A breadth cannot be negative, so x = 7 m. Thus option B is correct, while the other options fail to produce the stated area with length 3x − 2.
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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