The length of a rectangle is 20 m more than its breadth. If the length is increased by 8 m and the breadth by 6 m, the new area becomes 3360 square metres. What was the original breadth of the rectangle?
Answer and explanation
Correct answer: 42 m
Let the original breadth be (x) m. Then the original length is (x+20) m. After the increases, the dimensions become (x+28) m and (x+6) m. Thus, (x+28)(x+6)=3360
, which gives x^2+34x-3192=0. Its roots are x=42 and x=-76. Since a rectangle cannot have a negative dimension, the original breadth is 42 m. Exam tip: In geometrical word problems, reject any negative root because dimensions must be positive.
Frequently asked questions
What is the correct answer to this question?
42 m
Why is this the correct answer?
Let the original breadth be (x) m. Then the original length is (x+20) m. After the increases, the dimensions become (x+28) m and (x+6) m. Thus, (x+28)(x+6)=3360
, which gives x^2+34x-3192=0. Its roots are x=42 and x=-76. Since a rectangle cannot have a negative dimension, the original breadth is 42 m. Exam tip: In geometrical word problems, reject any negative root because dimensions must be positive.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Word Problems and Applications.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
