In a three-part square model, the side is (a+b+c). What is the total area of only the small squares?
Answer and explanation
Correct answer: (a^2+b^2+c^2)
A square whose side is split into parts of lengths \(a\), \(b\), and \(c\) contains three small square regions: one with side \(a\), one with side \(b\), and one with side \(c\). The area of a square is side multiplied by itself, so these three areas are \(a^2\), \(b^2\), and \(c^2\). The question asks only for the small squares, not for the rectangular regions between them.
Adding the three square areas gives \(a^2+b^2+c^2\). The terms \(ab\), \(bc\), and \(ca\) describe rectangular areas, and their doubled sum belongs to the cross terms in the full expansion of \((a+b+c)^2\). Therefore, option A correctly represents the total area of only the small squares. The complete model would also include the rectangular parts, but they must not be included here.
Frequently asked questions
What is the correct answer to this question?
(a^2+b^2+c^2)
Why is this the correct answer?
A square whose side is split into parts of lengths \(a\), \(b\), and \(c\) contains three small square regions: one with side \(a\), one with side \(b\), and one with side \(c\). The area of a square is side multiplied by itself, so these three areas are \(a^2\), \(b^2\), and \(c^2\). The question asks only for the small squares, not for the rectangular regions between them.
Adding the three square areas gives \(a^2+b^2+c^2\). The terms \(ab\), \(bc\), and \(ca\) describe rectangular areas, and their doubled sum belongs to the cross terms in the full expansion of \((a+b+c)^2\). Therefore, option A correctly represents the total area of only the small squares. The complete model would also include the rectangular parts, but they must not be included here.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Visual models of identities.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
