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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 l... 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

The perimeter of the pentagon is calculated by adding all its sides:

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

Combining like terms, we simplify:

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

[ 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 ( s ). The perimeter of the square is given by:

[ P_{square} = 4s ]

Step 3

Set the Perimeters Equal to Each Other

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Answer

Since the perimeter of the pentagon is equal to the perimeter of the square, we have:

[ 28x + 8 = 4s ]

Step 4

Solve for s

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Answer

Rearranging the equation to solve for ( s ):

[ 4s = 28x + 8 ]

Dividing both sides by 4 gives:

[ s = 7x + 2 ]

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