GCSE OCR Maths 3D trigonometry: The diagram shows two rectangles

The diagram shows two rectangles, A and B - OCR - GCSE Maths - Question 22 - 2019 - Paper 1

Question 22

The diagram shows two rectangles, A and B. Rectangle A has a width of 25 cm and a height of 12 cm. The width of rectangle B is three times the height of rectangle B... show full transcript

Worked Solution & Example Answer:The diagram shows two rectangles, A and B - OCR - GCSE Maths - Question 22 - 2019 - Paper 1

Step 1

Calculate the area of rectangle A

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Answer

The area of rectangle A can be calculated using the formula for the area of a rectangle, which is:

ext{Area} = ext{width} imes ext{height}

Substituting the given values:

ext{Area of Rectangle A} = 25 ext{ cm} imes 12 ext{ cm} = 300 ext{ cm}^2

Step 2

Express the dimensions of rectangle B

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Answer

Let the height of rectangle B be denoted as $h$ . Then, the width of rectangle B will be three times the height:

ext{Width of Rectangle B} = 3h

Step 3

Set up the equation for the areas

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Answer

Since the area of rectangle A is equal to the area of rectangle B, we have:

300 ext{ cm}^2 = ext{Width of Rectangle B} imes ext{Height of Rectangle B} = (3h)h = 3h^2

Step 4

Solve for h

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Answer

Rearranging the equation gives:

3h^2 = 300

Dividing by 3:

h^2 = 100

Taking the square root:

h = 10 ext{ cm}

Step 5

Find the width of rectangle B

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Answer

Using the value of height, we can find the width:

ext{Width of Rectangle B} = 3h = 3 imes 10 ext{ cm} = 30 ext{ cm}

Step 6

Calculate the perimeter of rectangle B

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Answer

The perimeter $P$ of a rectangle is given by the formula:

P = 2( ext{Width} + ext{Height})

Substituting the values:

P = 2(30 ext{ cm} + 10 ext{ cm}) = 2(40 ext{ cm}) = 80 ext{ cm}

The diagram shows two rectangles, A and B - OCR - GCSE Maths - Question 22 - 2019 - Paper 1

Worked Solution & Example Answer:The diagram shows two rectangles, A and B - OCR - GCSE Maths - Question 22 - 2019 - Paper 1

Calculate the area of rectangle A

Express the dimensions of rectangle B

Set up the equation for the areas

Solve for h

Find the width of rectangle B

Calculate the perimeter of rectangle B

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