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Here is a right-angled triangle - OCR - GCSE Maths - Question 20 - 2018 - Paper 1

Question 20

Here is a right-angled triangle. Not to scale Work out the value of x. The triangle has one side measuring 30 cm and another side measuring 8.4 cm. The side x cm ... show full transcript

Worked Solution & Example Answer:Here is a right-angled triangle - OCR - GCSE Maths - Question 20 - 2018 - Paper 1

Step 1

Use Pythagoras' Theorem

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Answer

To find the length of side x in a right-angled triangle, we apply Pythagoras' theorem, which states that the square of the hypotenuse (longest side) is equal to the sum of the squares of the other two sides. Here, we can denote the sides as follows:

Let:

a = 8.4 cm (one side)
b = x cm (the other side)
c = 30 cm (the hypotenuse)

Thus, the equation is:

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

Substituting our values gives:

$30^2 = 8.4^2 + x^2$

Step 2

Calculate and Solve for x

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Answer

Now, we compute the squares:

$30^2 = 900$ $8.4^2 = 70.56$

Substituting these into the equation:

$900 = 70.56 + x^2$

To isolate $x^2$ , we subtract 70.56 from both sides:

$x^2 = 900 - 70.56$ $x^2 = 829.44$

Next, we take the square root of both sides to solve for x:

$x = ext{√}(829.44)$

Calculating this yields:

$x ≈ 28.8$

Step 3

Final Answer

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Answer

Thus, the value of x is approximately 28.8 cm.

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