Question

what is the perimeter of the triangle. i do not know how to start this problem. any help will be greatly appreciated :))

Answer 1

Given:

Point F,G,H are midpoints of the sides of the triangle CDE.

`FG=9,GH=7,CD=24`

To find:

The perimeter of the triangle CDE.

Solution:

According to the triangle mid-segment theorem, the length of the mid-segment of a triangle is always half of the base of the triangle.

FG is mid-segment and DE is base. So, by using triangle mid-segment theorem, we get

`(1)/(2)DE=FG`

`DE=2(FG)`

`DE=2(9)`

`DE=18`

GH is mid-segment and CE is base. So, by using triangle mid-segment theorem, we get

`(1)/(2)CE=GH`

`CE=2(GH)`

`CE=2(7)`

`CE=14`

Now, the perimeter of the triangle CDE is:

`Perimeter=CD+DE+CE`

`Perimeter=24+18+14`

`Perimeter=56`

Therefore, the perimeter of the triangle CDE is 56 units.