Answer :
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Explanation :
- This is Right Angled Trian1gle.
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Solution :
- We'll solve this using the Pythagorean Theorem.
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Where,
- VW (9 mm) is the Hypotenuse.
- UW is the Perpendicular .
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We know that,
[tex]{\longrightarrow \pmb{\mathbb {\qquad (UV) {}^{2} + (UW) {}^{2} =( VW) {}^{2} }}} \\ \\ [/tex]
Now, we will substitute the given values in the formula :
[tex]{\longrightarrow \pmb{\sf {\qquad (6) {}^{2} + (UW) {}^{2} =( 9) {}^{2} }}} \\ \\ [/tex]
We know that, (6)² = 36 and (9)² = 81. So,
[tex]{\longrightarrow \pmb{\sf {\qquad 36 + (UW) {}^{2} =81}}} \\ \\ [/tex]
Now, transposing 36 to the other side we get :
[tex]{\longrightarrow \pmb{\sf {\qquad (UW) {}^{2} =81 - 36 }}} \\ [/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad (UW) {}^{2} = 45}}} \\ \\ [/tex]
Now, we'll take the square root of both sides to remove the square from UW :
[tex]{\longrightarrow \pmb{\sf {\qquad \sqrt{(UW) {}^{2}} = \sqrt{ 45}}}} \\ \\ [/tex]
When we take the square root of (UW)² , it becomes UW,
[tex]{\longrightarrow \pmb{\sf {\qquad UW = \sqrt{45}}}} \\ \\ [/tex]
We know that, square root of 45 is 6.708.
[tex]{\longrightarrow \pmb{\sf {\qquad UW \approx6.708}}} \\ \\ [/tex]
So,
- The measure of the missing side (UW) is 6.7 mm (Rounded to nearest tenth)
