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

Question

asked Jul 21, 2023 65.4k views

1 Answer

Nicolas Cortot · Answer 1 · 2023-07-25T11:53:44+0000

Answer :

$\:$

Explanation :

$\:$

Solution :

$\:$

Where,

$\:$

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)