Question

Math

Posted 4 months ago

```
Find the perimeter of $\triangle S O W$.
If entering your answer as a decimal, round your final answer to the nearest hundredth.
units
```

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Answer from Sia

Posted 4 months ago

Solution by Steps

step 1

Identify the lengths of the sides of the triangle ΔSWO

step 2

The lengths are given as SN = 8 units, SO = 10 units, and NO = 6 units

step 3

To find the perimeter of ΔSWO, add the lengths of the sides SN, SO, and the full length of SW

step 4

Since NO is a dashed line and there is a right angle where line NO meets line SW, we infer that ΔSNO is a right triangle

step 5

Use the Pythagorean theorem to find the length of SW: $SW = \sqrt{SN^2 + NW^2} = \sqrt{8^2 + 6^2}$

step 6

Calculate SW: $SW = \sqrt{64 + 36} = \sqrt{100} = 10$ units

step 7

Now, add the lengths of SN, SO, and SW to find the perimeter: $Perimeter = SN + SO + SW = 8 + 10 + 10$

step 8

Calculate the perimeter: $Perimeter = 28$ units

[1] Answer

The perimeter of $ΔSOW$ is 28 units.

Key Concept

Finding the perimeter of a triangle

Explanation

The perimeter of a triangle is the sum of the lengths of its sides. For right triangles, the Pythagorean theorem can be used to find the length of the hypotenuse if the lengths of the other two sides are known.

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