An \(x\) by \(x\) square, two \(x\) by \(5\) rectangles, and one \(5\) by \(5\) square are combined. This is a model of what?
Answer and explanation
Correct answer: \((x+5)^2\)
The \(x\) by \(x\) square has area \(x^2\). The two \(x\) by \(5\) rectangles together have area \(5x+5x=10x\), and the \(5\) by \(5\) square has area \(25\). Thus, the total area is \(x^2+10x+25=(x+5)^2\). In contrast, \((x-5)^2\) has the middle term \(-10x\), so it does not match. Exam tip: add the areas of the two equal rectangles first to identify the middle term.
Frequently asked questions
What is the correct answer to this question?
\((x+5)^2\)
Why is this the correct answer?
The \(x\) by \(x\) square has area \(x^2\). The two \(x\) by \(5\) rectangles together have area \(5x+5x=10x\), and the \(5\) by \(5\) square has area \(25\). Thus, the total area is \(x^2+10x+25=(x+5)^2\). In contrast, \((x-5)^2\) has the middle term \(-10x\), so it does not match. Exam tip: add the areas of the two equal rectangles first to identify the middle term.
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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