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The perimeter of the pentagon is equal to the perimeter of the square - OCR - GCSE Maths - Question 16 - 2018 - Paper 1

Question 16

The perimeter of the pentagon is equal to the perimeter of the square. Not to scale 5x + 3 7x + 4 2x + 3 9x - 10 5x + 8 Find an expression for the length of one s... show full transcript

Worked Solution & Example Answer:The perimeter of the pentagon is equal to the perimeter of the square - OCR - GCSE Maths - Question 16 - 2018 - Paper 1

Step 1

Find the perimeter of the pentagon

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Answer

To find the perimeter of the pentagon, we add the expressions for each side:

$P_{pentagon} = (5x + 3) + (7x + 4) + (2x + 3) + (9x - 10) + (5x + 8)$

This simplifies to:

$P_{pentagon} = 5x + 7x + 2x + 9x + 5x + (3 + 4 + 3 - 10 + 8)$

So,

$P_{pentagon} = 28x + 8$

Step 2

Find the perimeter of the square

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Answer

Let the length of one side of the square be denoted as $s$ . The perimeter of the square is given by:

$P_{square} = 4s$

Step 3

Set the perimeters equal and solve for s

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Answer

Since the perimeter of the pentagon is equal to the perimeter of the square, we can equate both expressions:

$28x + 8 = 4s$

Now, solving for $s$ :

$s = \frac{28x + 8}{4}$

This further simplifies to:

$s = 7x + 2$

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