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Pythagoras' Theorem 2

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5

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4

10

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Easier question

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Find the length of the side marked 𝑥. Give your answer correct to 3 significant figures.

Find the length of the side marked 𝑥

Is the side marked 𝑥 the longest side or is it one of the two shorter sides?

7cm

𝑥

10cm

𝑥

5cm

𝑥

7cm

𝑥

5cm

10cm

𝑥

𝑥

5cm

𝑥

10cm

𝑥

𝑥

7cm

10cm

𝑥

5cm

𝑥

𝑥

7cm

cm

Longest
Shorter
Longest
Shorter
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Correct

This is not correct.
We are finding one of the two shorter sides, so we need to find

the difference between the squares of the two given sides.


𝑥² = 25² − 11²
    = 625 − 121
    = 504
𝑥 = √504
   = 22.4cm  (to 3 s.f.)

This is not correct.
We are finding the hypotenuse, so we need to

add the squares of the two given sides.


𝑥² = 10² + 6²
    = 100 + 36
    = 136
𝑥 = √136
   = 11.7cm  (to 3 s.f.)

This is not correct.

The side marked 𝑥 is opposite the right angle

(it is the hypotenuse), so it is the longest side.

This is not correct.

The side marked 𝑥 is one of the two sides that have the right angle

between them, so it is one of the two shorter sides.

The side marked 𝑥 is one of the two sides that have the right angle

between them, so it is one of the two shorter sides.

The side marked 𝑥 is opposite the right angle

(it is the hypotenuse), so it is the longest side.

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