Question

Solve for the missing side. round to the nearest 10th.

Answer 1

• 6.7 mm

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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.

• UV (6 mm) is the Base.

• UW is the Perpendicular .

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We know that,

`{\longrightarrow \pmb{\mathbb {\qquad (UV) {}^(2) + (UW) {}^(2) =( VW) {}^(2) }}} \\ \\`

Now, we will substitute the given values in the formula :

`{\longrightarrow \pmb{\sf {\qquad (6) {}^(2) + (UW) {}^(2) =( 9) {}^(2) }}} \\ \\`

We know that, (6)² = 36 and (9)² = 81. So,

`{\longrightarrow \pmb{\sf {\qquad 36 + (UW) {}^(2) =81}}} \\ \\`

Now, transposing 36 to the other side we get :

`{\longrightarrow \pmb{\sf {\qquad (UW) {}^(2) =81 - 36 }}} \\`

`{\longrightarrow \pmb{\sf {\qquad (UW) {}^(2) = 45}}} \\ \\`

Now, we'll take the square root of both sides to remove the square from UW :

`{\longrightarrow \pmb{\sf {\qquad \sqrt{(UW) {}^(2)} = √( 45)}}} \\ \\`

When we take the square root of (UW)² , it becomes UW,

`{\longrightarrow \pmb{\sf {\qquad UW = √(45)}}} \\ \\`

We know that, square root of 45 is 6.708.

`{\longrightarrow \pmb{\sf {\qquad UW \approx6.708}}} \\ \\`

So,

• The measure of the missing side (UW) is 6.7 mm (Rounded to nearest tenth)