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Find the Incorrect Area Expression for a Rectangle with Length x+y and Width 4
Mathematics
Grade 7
Question Content
Circle the expression that does not represent the area of the outside shaded rectangle. Write its letter in the corresponding numbered box. The rectangle has length x+y and width 4. Options: S. 4(x + y), K. 4x + 4y, T. 4 + xy
Correct Answer
T
Detailed Solution Steps
1
Step 1: Calculate the area of the large rectangle using the formula Area = length × width. Here, length = x+y, width = 4, so Area = 4(x+y).
2
Step 2: Use the distributive property to expand 4(x+y), which gives 4x + 4y.
3
Step 3: Compare with the options. 4+xy does not equal the area of the large rectangle, so this is the incorrect expression.
Knowledge Points Involved
1
Area of a Rectangle
The area of a rectangle is calculated by multiplying its length by its width, expressed as A = l×w. This formula is used to find the total space enclosed by the rectangle's sides.
2
Distributive Property
The distributive property states that a(b+c) = ab+ac. It is used to expand algebraic expressions by distributing the term outside the parentheses to each term inside.
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