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

$\dfrac{1}{2}DE=FG$

$DE=2(FG)$

$DE=2(9)$

$DE=18$

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

$\dfrac{1}{2}CE=GH$

$CE=2(GH)$

$CE=2(7)$

$CE=14$

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.