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In this question, all lengths are in centimetres - OCR - GCSE Maths - Question 24 - 2019 - Paper 1

Question 24

In this question, all lengths are in centimetres. Here is a square. 4a + 2b 6a + b - 1 Find the length of one side of the square when b = 4.

Worked Solution & Example Answer:In this question, all lengths are in centimetres - OCR - GCSE Maths - Question 24 - 2019 - Paper 1

Step 1

Substituting b = 4

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Answer

Start by substituting the value of b into the expressions for the side length.

For the left side, substituting gives us:

$4a + 2(4) = 4a + 8$

For the top side:

$6a + (4) - 1 = 6a + 3$

Step 2

Setting the sides equal

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Answer

Since both expressions represent the length of a side of the square, we set them equal to each other:

$4a + 8 = 6a + 3$

Step 3

Solving for a

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Answer

To solve for a, rearrange the equation:

$4a + 8 - 3 = 6a$

This simplifies to:

$5 = 6a - 4a$ $5 = 2a$

Now divide both sides by 2:

$a = rac{5}{2} = 2.5$

Step 4

Finding the length of one side

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Answer

Finally, substitute a back into one of the expressions to find the length of one side of the square:

Using the expression for the left side:

$4(2.5) + 8 = 10 + 8 = 18$

Thus, the length of one side of the square is 18 cm.

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