The length of a rectangle is 3 units more than its breadth, and its area is 70 square units. What is the length of the rectangle?
Answer and explanation
Correct answer: 10 units
Let the breadth be \(x\) units. Then the length is \(x+3\) units, so \(x(x+3)=70\), or \(x^2+3x-70=0\). Factoring gives \((x+10)(x-7)=0\). Since a breadth must be positive, \(x=7\), and the length is \(7+3=10\) units. The root \(-10\) is not physically meaningful. Exam tip: In geometry word problems, reject roots that make a length or breadth negative.
Frequently asked questions
What is the correct answer to this question?
10 units
Why is this the correct answer?
Let the breadth be \(x\) units. Then the length is \(x+3\) units, so \(x(x+3)=70\), or \(x^2+3x-70=0\). Factoring gives \((x+10)(x-7)=0\). Since a breadth must be positive, \(x=7\), and the length is \(7+3=10\) units. The root \(-10\) is not physically meaningful. Exam tip: In geometry word problems, reject roots that make a length or breadth negative.
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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