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Here is a right-angled triangle - OCR - GCSE Maths - Question 18 - 2019 - Paper 1

Question 18

Here is a right-angled triangle. 12 cm x cm 18 cm Work out the value of x. x =

Worked Solution & Example Answer:Here is a right-angled triangle - OCR - GCSE Maths - Question 18 - 2019 - Paper 1

Step 1

Step 1: Use the Pythagorean Theorem

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Answer

For a right-angled triangle, the Pythagorean theorem states that: $c^2 = a^2 + b^2$ where 'c' is the hypotenuse, and 'a' and 'b' are the other two sides. Here, the hypotenuse is 18 cm, and one side is 12 cm.

Let x be the second side.

Thus, the equation becomes: $18^2 = 12^2 + x^2$

Step 2

Step 2: Calculate the squares

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Answer

Calculating the squares gives us: $324 = 144 + x^2$

Step 3

Step 3: Solve for x

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Answer

We can solve for x^2 by rearranging the equation: $x^2 = 324 - 144$ $x^2 = 180$

Taking the square root of both sides yields:

ewline ext{sqrt}(180) = ext{sqrt}(36 imes 5) = 6 ext{sqrt}(5) ext{ cm}$$

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