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Here is a right-angled triangle - Edexcel - GCSE Maths - Question 6 - 2021 - Paper 2

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Here is a right-angled triangle. The shaded shape below is made from two of these triangles. Work out the perimeter of the shaded shape. Give your answer correct t... show full transcript

Worked Solution & Example Answer:Here is a right-angled triangle - Edexcel - GCSE Maths - Question 6 - 2021 - Paper 2

Step 1

Step 1: Find the length of the hypotenuse

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Answer

To find the length of the hypotenuse of the right-angled triangle, we use the Pythagorean theorem:

c=a2+b2c = \sqrt{a^2 + b^2} Where:

  • a = 8 mm
  • b = 10 mm

Therefore:

c=82+102=64+100=164c = \sqrt{8^2 + 10^2} = \sqrt{64 + 100} = \sqrt{164}

Calculating this gives: c≈12.81 mmc \approx 12.81 \text{ mm}

Step 2

Step 2: Calculate the perimeter of the shaded shape

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Answer

The shaded shape consists of two triangles. The perimeter can be calculated as follows:

Perimeter = Base + Height + (2 × Hypotenuse)

  • Base = 10 mm
  • Height = 8 mm
  • Hypotenuse = 164≈12.81\sqrt{164} \approx 12.81 mm (from Step 1)

Substituting in the values:

P=10+8+2×12.81P = 10 + 8 + 2 \times 12.81

Calculating this gives: P≈10+8+25.62=43.62 mmP \approx 10 + 8 + 25.62 = 43.62 \text{ mm}

Rounding to 3 significant figures gives: P≈43.6 mmP \approx 43.6 \text{ mm}

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