Points J and K are midpoints of the sides of triangle FGH. What is the value of y?
J and K are the midpoints of the sides ΔFGH.
Line segments GJ and JH are congruent.
Line segments HK and KF are congruent.
The Length of JK is 2y + 5 and the length of GF is 5y + 3. What is the value of y?

Solution:

Points J and K are midpoints of the sides of triangle FGH

Given, J and K are midpoints of the sides of triangle FGH.

JK = (2y + 5)

GF = (5y + 3)

We have to find the value of y.

Thales theorem states that "the line drawn parallel to one side of a triangle and cutting the other two sides divides the other two sides in equal proportion"

From the figure, HKJ and FGH are similar. JK and GF are parallel.

So, HK / HF = HJ / HG = KJ / GF ---------- (1)

We know, HK = HF / 2

HF = 2HK

Use HF = 2HK in (1)

HK / 2HK = JK / GF

1 / 2 = (2y + 5)/(5y + 3)

On rearranging,

5y + 3 = 2(2y + 5)

5y + 3 = 4y + 10

Grouping of common terms,

5y - 4y = 10 - 3

y = 7

Therefore, the value of y is 7units.

Points J and K are midpoints of the sides of triangle FGH. What is the value of y?

Summary:

Points J and K are midpoints of the sides of triangle FGH. The value of y is 7 units.

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