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The diagram shows two right-angled triangles ACB and DEB - Edexcel - GCSE Maths - Question 11 - 2021 - Paper 3

Question 11

The diagram shows two right-angled triangles ACB and DEB. AD = 9 cm DE = 2 cm DB = 6 cm Calculate the length of CB. Give your answer correct to 2 decimal places. ... show full transcript

Worked Solution & Example Answer:The diagram shows two right-angled triangles ACB and DEB - Edexcel - GCSE Maths - Question 11 - 2021 - Paper 3

Step 1

Calculate the length of DE:

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Answer

Since DE = 2 cm and DB = 6 cm, we need to find the length of EB first. By the right triangle properties, we know:

declared is that we have the length AD = 9 cm and the length DE = 2 cm, therefore the length AE can be found out as follows:

Using Pythagoras’ theorem:

$AE = ext{AD} - ext{DE} = 9 ext{ cm} - 2 ext{ cm} = 7 ext{ cm}$

Step 2

Using Pythagoras' theorem to find CB:

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Answer

For triangle ACB, we can apply Pythagoras’ theorem.

Let CB be the hypotenuse, therefore:

$AC^2 + CB^2 = AB^2$

Where:

AC = AE = 7 cm
AB = DB + DE = 6 cm + 2 cm = 8 cm

So we get:

$7^2 + CB^2 = 8^2$

This simplifies to:

$49 + CB^2 = 64$

Now we solve for CB^2:

$CB^2 = 64 - 49$
$CB^2 = 15$

Taking the square root of both sides:

$CB = ext{√}15 ext{ cm} ≈ 3.87 ext{ cm}$

Rounding to 2 decimal places gives: 3.87 cm.

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