Question

Given: തതതത is a midsegment of ∆. Show all work.

a. Find the value of x and y.
b. What is the length of തതതത?

Answer 1

Explanation:

since it is a mid-segment, DGH and DEF are similar triangles with the constant scaling factor of 2 for the lengths of all sides and other lines in the triangle.

e.g.

DE = 2 × DG

DF = 2 × DH

and therefore,

28 = 2 × GH = 2× (x - 3)

14 = x - 3

x = 17

HF = x - 7 = 17 - 7 = 10

DH = HF = 10

so,

y + 8 = 10

y = 2

and DF = 10 + 10 = 20