A square of side (5) is removed from a large square of side (z) and the remaining area is rearranged as a rectangle. What can be the sides of the rectangle?
Answer and explanation
Correct answer: Sides \(z-5\) and \(z+5\)
The area of the large square is \(z^2\), while the removed square has area \(5^2=25\). Thus, the remaining area is \(z^2-25\). Using the difference of squares identity, \(z^2-25=(z-5)(z+5)\). Hence, the rectangle can have sides \(z-5\) and \(z+5\). The sides \(z-5\) and \(z-5\) would give \((z-5)^2\), which is not equal to \(z^2-25\). Exam tip: recognise \(a^2-b^2=(a-b)(a+b)\) before expanding expressions.
Frequently asked questions
What is the correct answer to this question?
Sides \(z-5\) and \(z+5\)
Why is this the correct answer?
The area of the large square is \(z^2\), while the removed square has area \(5^2=25\). Thus, the remaining area is \(z^2-25\). Using the difference of squares identity, \(z^2-25=(z-5)(z+5)\). Hence, the rectangle can have sides \(z-5\) and \(z+5\). The sides \(z-5\) and \(z-5\) would give \((z-5)^2\), which is not equal to \(z^2-25\). Exam tip: recognise \(a^2-b^2=(a-b)(a+b)\) before expanding expressions.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Visual models of identities.
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