The diagram shows a quadrilateral and an equilateral triangle - OCR - GCSE Maths - Question 16 - 2023 - Paper 1
Question 16
The diagram shows a quadrilateral and an equilateral triangle.
The perimeter of the quadrilateral is equal to the perimeter of the equilateral triangle.
5x + 4
6x... show full transcript
Worked Solution & Example Answer:The diagram shows a quadrilateral and an equilateral triangle - OCR - GCSE Maths - Question 16 - 2023 - Paper 1
Step 1
Step 1: Calculate the perimeter of the quadrilateral
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Answer
To find the perimeter of the quadrilateral, we sum up all its sides:
extPerimeterextquad=(5x+4)+(6x+8)+(x+2)+(9x−5)
This simplifies to:
=5x+6x+x+9x+4+8+2−5=21x+9
Step 2
Step 2: Calculate the perimeter of the equilateral triangle
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Answer
The perimeter of the equilateral triangle is three times the length of one side:
extPerimeterexttriangle=3s
where s is the length of one side.
Step 3
Step 3: Set the perimeters equal to each other
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Answer
According to the problem, the perimeters are equal:
21x+9=3s
Step 4
Step 4: Solve for $s$
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Answer
Rearranging the equation to find s gives us:
s = rac{21x + 9}{3}
Simplifying further:
s=7x+3
Step 5
Final Answer
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Answer
The expression for the length of one side of the equilateral triangle in terms of x is:
