Question

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A polygon is regular if each of its sides has the same length. Find the perimeter of the regular polygon.

Answer 1

Here we go !!

Since it's a regular pentagon, all it's sides are equal so let's solve for x

`\hookrightarrow \: 3(x - 1) = 5x - 6`

`\hookrightarrow \: 3x - 3 = 5x - 6`

`\hookrightarrow \: 3x - 5x = - 6 + 3`

`\hookrightarrow \: - 2x = - 3`

`\hookrightarrow \: x = ( - 3)/( - 2)`

`\boxed{\boxed{x = (3)/(2) }}`

now let's find the measure of each side, i.e

`\hookrightarrow \: 5x - 6`

`\hookrightarrow \: (5 * (3)/(2)) - 6`

`\hookrightarrow \: (15)/(2) - 6`

`\hookrightarrow \: 7.5 - 6`

`\mathrm{\hookrightarrow \: 1.5 \: units}`

perimeter = 5 × side length ( for a regular pentagon )

`\hookrightarrow \: 1.5 * 5`

`\boxed{ \boxed{ \: \: \: \: \: \: \: \: 7.5 \: \: units \: \: \: \: \: \: \: }}`