A visual model of a square with side 2a + 5 will show which area parts?
Answer and explanation
Correct answer: 4a², 20a, 25
The governing concept is the visual form of the identity (p + q)² = p² + 2pq + q². A square whose side is divided into lengths p and q contains one p-by-p square, two p-by-q rectangles, and one q-by-q square. Here p = 2a and q = 5. The first square has area (2a)² = 4a². Each rectangle has area (2a)(5) = 10a, so the two rectangles together have area 20a. The final small square has area 5² = 25. Therefore the model shows 4a², 20a, and 25, so option B is correct. Option A counts only one rectangle; C gives an incorrect first area; and D gives an incorrect constant and middle contribution.
Frequently asked questions
What is the correct answer to this question?
4a², 20a, 25
Why is this the correct answer?
The governing concept is the visual form of the identity (p + q)² = p² + 2pq + q². A square whose side is divided into lengths p and q contains one p-by-p square, two p-by-q rectangles, and one q-by-q square. Here p = 2a and q = 5. The first square has area (2a)² = 4a². Each rectangle has area (2a)(5) = 10a, so the two rectangles together have area 20a. The final small square has area 5² = 25. Therefore the model shows 4a², 20a, and 25, so option B is correct. Option A counts only one rectangle; C gives an incorrect first area; and D gives an incorrect constant and middle contribution.
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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