The perimeter of a rectangle is (112) cm and its length is (16) cm more than its breadth. What is the area of the rectangle?
Answer and explanation
Correct answer: \(720\ \text{cm}^2\)
Let the length be \(l\) cm and the breadth be \(b\) cm. From the perimeter, \(2(l+b)=112\), so \(l+b=56\). Also, \(l-b=16\). Adding the two equations gives \(2l=72\), hence \(l=36\) and \(b=20\). Therefore, the area is \(l\times b=36\times20=720\ \text{cm}^2\). A choice such as \(700\ \text{cm}^2\) is not the product of the correct length and breadth. Exam tip: In rectangle-perimeter questions, first convert \(2(l+b)\) carefully into \(l+b\).
Frequently asked questions
What is the correct answer to this question?
\(720\ \text{cm}^2\)
Why is this the correct answer?
Let the length be \(l\) cm and the breadth be \(b\) cm. From the perimeter, \(2(l+b)=112\), so \(l+b=56\). Also, \(l-b=16\). Adding the two equations gives \(2l=72\), hence \(l=36\) and \(b=20\). Therefore, the area is \(l\times b=36\times20=720\ \text{cm}^2\). A choice such as \(700\ \text{cm}^2\) is not the product of the correct length and breadth. Exam tip: In rectangle-perimeter questions, first convert \(2(l+b)\) carefully into \(l+b\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Algebraic methods: Substitution method and Elimination method..
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