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The diagram shows two rectangles, A and B - Edexcel - GCSE Maths - Question 13 - 2021 - Paper 1

Question 13

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 13 - 2021 - Paper 1

Step 1

Step 1: Find the Area of Rectangle A

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Answer

The area of rectangle A can be calculated using the formula for the area of a rectangle, which is length times width. In this case, the length is 2w + y, and the width is 6. Therefore, the area of rectangle A is:

$ext{Area}_A = (2w + y) imes 6 = 12w + 6y$

Step 2

Step 2: Find the Area of Rectangle B

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Answer

Similarly, for rectangle B, the length is 7w and the width is (3 + 6). Thus, the area of rectangle B is:

$ext{Area}_B = 7w imes (3 + 6) = 7w imes 9 = 63w$

Step 3

Step 3: Set the Areas Equal

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Answer

Since the areas of rectangles A and B are equal, we can set up the following equation:

$12w + 6y = 63w$

Step 4

Step 4: Solve for y

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Answer

Now we isolate y in the equation. First, subtract 12w from both sides:

$6y = 63w - 12w$

This simplifies to:

$6y = 51w$

Next, divide both sides by 6:

$y = rac{51w}{6}$

Thus, we have found an expression for y in terms of w:

$y = rac{17w}{2}$

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