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Here is a right-angled triangle - Edexcel - GCSE Maths - Question 9 - 2021 - Paper 2

Question 9

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 9 - 2021 - Paper 2

Step 1

Find the hypotenuse of the triangle

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Answer

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

$c^2 = a^2 + b^2$

Here, $a = 8$ mm and $b = 10$ mm. Thus,

$c^2 = 8^2 + 10^2 = 64 + 100 = 164$

So, the hypotenuse is:

$c = ext{sqrt}(164) \approx 12.81 ext{ mm}$

Step 2

Find the perimeter of the shaded shape

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Answer

The shaded shape consists of 2 triangles. The perimeter of the shaded shape can be found by adding the lengths of all the sides:

The lengths are:

Base: 10 mm
Height on one side: 8 mm
Height on the other side: 8 mm
Hypotenuse from both triangles: 12.81 mm

Thus, the total perimeter is:

$P = 10 + 8 + 12.81 = 30.81 \text{ mm}$

Rounding to 3 significant figures, the perimeter is:

$P \approx 30.8 \text{ mm}$

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