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 + 8 x + 2 9x - 5 Find an expression for the length of one side of the equilateral triangle. Give your answer in terms of x in its simplest form.

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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

Find the Perimeter of the Quadrilateral

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Answer

To find the perimeter of the quadrilateral, we add the lengths of all its sides:

$P_{quadrilateral} = (5x + 4) + (6x + 8) + (x + 2) + (9x - 5)$

Simplifying this:

$P_{quadrilateral} = 5x + 6x + x + 9x + 4 + 8 + 2 - 5$

This equals:

$P_{quadrilateral} = 21x + 9$

Step 2

Find 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, which we can denote as S:

$P_{triangle} = 3S$

Step 3

Set the Perimeters Equal

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Answer

Since the perimeters are equal, we can set the two expressions equal to each other:

$21x + 9 = 3S$

To find S, we can rearrange this equation:

$S = \frac{21x + 9}{3}$

Step 4

Simplify the Expression for S

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Answer

Now we will simplify the expression for S:

$S = 7x + 3$

Thus, the expression for the length of one side of the equilateral triangle in terms of x is:

Answer:

$S = 7x + 3$

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