Question

I need helppp pp p pp p p

Answer 1

`\text{In terms of Gazebos, the perimeter of Gazebo A = \textbf{46 m}}`

Explanation:

Since the two pentagons are similar the ratio of each side of the smaller pentagon to the corresponding side of the larger pentagon is the same

We are given that in pentagon ABCDE, side AB = 10 and the corresponding side FG of pentagon FGHJK = 15

`\text{Therefore } \\\\\frac{\overline {AB}}{\overline{FG}} =(10)/(15) = (2)/(3)$ \textrm(divide numerator and denominator by 5)}\\`

The ratios of all the other sides of ABCDE to the corresponding sides of FGHJK must also be
`\displaystyle {(2)/(3)}`

Therefore it follows that the perimeter of ABCDE = 2/3 x perimeter of FGHJK

Perimeter of FGHJK = sum of sides
`= 15 + 9 + 12 + 15 + 18 = 69 \;m`

`\textrm{Perimeter of ABCDE } = (2)/(3) \cdot 69 = 2 \cdot 23 = 46\text{ m}\\\\`

`\text{In terms of Gazebos, the perimeter of Gazebo A = \textbf{46 m}}`