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The diagram shows two rectangles, A and B - Edexcel - GCSE Maths - Question 12 - 2021 - Paper 1

Question 12

The diagram shows two rectangles, A and B. All measurements are in centimetres. The area of rectangle A is equal to the area of rectangle B. Find an expression fo... show full transcript

Worked Solution & Example Answer:The diagram shows two rectangles, A and B - Edexcel - GCSE Maths - Question 12 - 2021 - Paper 1

Step 1

Write the expressions for the areas of rectangles A and B

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Answer

The area of rectangle A can be expressed as: $A = ext{length} imes ext{width} = 6(2w + y)$

The area of rectangle B can be expressed as: $B = ext{length} imes ext{width} = 7w(3 + 6)$

Step 2

Set the areas equal to each other

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Answer

Since the areas of rectangle A and B are equal, we can set up the equation: $6(2w + y) = 7w(3 + 6)$

Step 3

Expand the equation

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Answer

Expanding both sides, we get: $12w + 6y = 7w(9)$ $12w + 6y = 63w$

Step 4

Rearrange to isolate y

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Answer

Rearranging the equation to solve for y: $6y = 63w - 12w$ $6y = 51w$ $y = rac{51w}{6}$

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