In this question, assume all dimensions are in centimetres. Jess and Pete have many rectangular tiles. Each tile has length $a + b$ and width $2b$. (a) Jess joins three tiles together to make a larger rectangle, as shown. (i) Write an expression for the perimeter of her rectangle. Give your answer in its simplest form. (ii) An expression for the area of her rectangle is $6ab + 6b^2$. Factorise this expression fully. (b) Pete joins some tiles together to make a different rectangle. The area of his rectangle is $8ab + 8b^2$. Draw a possible arrangement of tiles for Pete's rectangle. Write down expressions for the length and the width of the rectangle.

GCSE OCR Maths Vectors: In this question, assume all dim

In this question, assume all dimensions are in centimetres - OCR - GCSE Maths - Question 13 - 2018 - Paper 1

Question 13

In this question, assume all dimensions are in centimetres. Jess and Pete have many rectangular tiles. Each tile has length $a + b$ and width $2b$. (a) Jess joins ... show full transcript

Worked Solution & Example Answer:In this question, assume all dimensions are in centimetres - OCR - GCSE Maths - Question 13 - 2018 - Paper 1

Step 1

Write an expression for the perimeter of her rectangle.

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Answer

To find the perimeter of a rectangle, we use the formula:

$P = 2(l + w)$

In Jess's case, the length is the total length of three tiles, which is: $ext{Length} = 3(a + b)$ And the width is: $ext{Width} = 2b$

Thus, the perimeter can be expressed as:

$P = 2(3(a + b) + 2b) = 2(3a + 3b + 2b) = 2(3a + 5b) = 6a + 10b.$

Step 2

An expression for the area of her rectangle is $6ab + 6b^2$. Factorise this expression fully.

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Answer

To factor the expression $6ab + 6b^2$ , we can factor out the common term:

$6ab + 6b^2 = 6b(a + b).$

Step 3

Draw a possible arrangement of tiles for Pete's rectangle.

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Answer

A possible arrangement for Pete's rectangle using the tiles would be:

4 tiles arranged in a row, giving:

$ext{Length} = 4(a + b), ext{Width} = 2b.$

Step 4

Write down expressions for the length and the width of the rectangle.

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Answer

For Pete's rectangle, the expressions are:

Length: $4(a + b)$
Width: $2b.$

In this question, assume all dimensions are in centimetres - OCR - GCSE Maths - Question 13 - 2018 - Paper 1

Worked Solution & Example Answer:In this question, assume all dimensions are in centimetres - OCR - GCSE Maths - Question 13 - 2018 - Paper 1

Write an expression for the perimeter of her rectangle.

An expression for the area of her rectangle is $6ab + 6b^2$. Factorise this expression fully.

Draw a possible arrangement of tiles for Pete's rectangle.

Write down expressions for the length and the width of the rectangle.

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