GCSE OCR Maths More factorising - quadratics: 22 In this question, all measure

22 In this question, all measurements are in centimetres - OCR - GCSE Maths - Question 22 - 2021 - Paper 3

Question 22

22 In this question, all measurements are in centimetres. The square and the rectangle have the same area. (a) Show that $x^2 - 8x - 20 = 0$. (b) Solve $x^2 - 8x... show full transcript

Worked Solution & Example Answer:22 In this question, all measurements are in centimetres - OCR - GCSE Maths - Question 22 - 2021 - Paper 3

Step 1

Show that $x^2 - 8x - 20 = 0$

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Answer

To show that the square and rectangle have the same area:

Calculate the area of the square:
- The side length of the square is $x$ , so the area is: $ext{Area}_{ ext{square}} = x^2$
Calculate the area of the rectangle:
- The width is 4 cm and the length is given by $2x + 5$ . Therefore, the area is: $ext{Area}_{ ext{rectangle}} = 4(2x + 5) = 8x + 20$
Set the areas equal: $x^2 = 8x + 20$
Rearrange the equation:
- Move all terms to one side: $x^2 - 8x - 20 = 0$
- This shows the required equation.

Step 2

Solve $x^2 - 8x - 20 = 0$

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Answer

To solve the equation $x^2 - 8x - 20 = 0$ , we can factor it:

Identify factors:
- We need two numbers that multiply to -20 and add to -8. These numbers are -10 and +2.
Factor the equation: $(x - 10)(x + 2) = 0$
Find the solutions:
- Set each factor to zero:
  - $x - 10 = 0$ or $x + 2 = 0$
- This gives:
  - $x = 10$ or $x = -2$
Write the final answer:
- Therefore, the solutions are: $x = 10$ or $x = -2$

22 In this question, all measurements are in centimetres - OCR - GCSE Maths - Question 22 - 2021 - Paper 3

Worked Solution & Example Answer:22 In this question, all measurements are in centimetres - OCR - GCSE Maths - Question 22 - 2021 - Paper 3

Show that $x^2 - 8x - 20 = 0$

Solve $x^2 - 8x - 20 = 0$

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