If two equal rectangles in an area model have areas 7x and 7x, what is the total middle term?
Answer and explanation
Correct answer: 14x
The governing idea is addition of areas and combination of like algebraic terms. In an area model, the two rectangles are separate parts, so their contributions are added rather than multiplied. Their areas are 7x and 7x, and both contain the same variable part x. Therefore, add their coefficients while retaining x: 7x+7x=(7+7)x=14x. Option C is correct. The answer is not 49x because that would incorrectly multiply 7 by 7 while leaving x unchanged; if multiplication were intended, the variable power would also need careful treatment. Option A gives only one rectangle’s area, not the total. Option D would represent a product of two x-length quantities, which is not what the stated area labels require.
Frequently asked questions
What is the correct answer to this question?
14x
Why is this the correct answer?
The governing idea is addition of areas and combination of like algebraic terms. In an area model, the two rectangles are separate parts, so their contributions are added rather than multiplied. Their areas are 7x and 7x, and both contain the same variable part x. Therefore, add their coefficients while retaining x: 7x+7x=(7+7)x=14x. Option C is correct. The answer is not 49x because that would incorrectly multiply 7 by 7 while leaving x unchanged; if multiplication were intended, the variable power would also need careful treatment. Option A gives only one rectangle’s area, not the total. Option D would represent a product of two x-length quantities, which is not what the stated area labels require.
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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