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Using Pythagoras' theorem, calculate the length of YZ.

Give your answer in centimetres (cm) to 1 d.p.
9 cm
17 cm
Z
Not drawn accurately

User Lkemitchll
by
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1 Answer

6 votes

Answer:

Certainly! To solve for the length of \(YZ\) using Pythagoras' theorem, we'll use the formula \(c^2 = a^2 + b^2\), where \(c\) is the hypotenuse (opposite the right angle) and \(a\) and \(b\) are the other two sides.

Given that the length of one side is \(9 \, \text{cm}\), and the length of the hypotenuse (Z) is \(17 \, \text{cm}\), let's denote the length of \(YZ\) as \(x\) (in centimeters).

So, applying Pythagoras' theorem:

\[17^2 = 9^2 + x^2\]

\[289 = 81 + x^2\]

\[x^2 = 289 - 81\]

\[x^2 = 208\]

To find \(x\), we take the square root of both sides:

\[x = \sqrt{208}\]

\[x \approx 14.4 \, \text{cm}\]

Therefore, the length of \(YZ\) is approximately \(14.4 \, \text{cm}\) to 1 decimal place when rounded.

User Lusketeer
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