Question

Points J and K are midpoints of the sides of triangle FGH. Triangle F G H is cut by lines segment J K. Point J is the midpoint of side G H. Point K is the midpoint of side H F. Line segments G J and J H are congruent. Line segments H K and K F are congruent. The Length of J K is 2 y + 5 and the length of G F is 5 y + 3.

What is the value of y?

Answer 1

Y = 7

Explanation:

100% CORRECT

Answer 2

Value of y = 7

Explanation:

By the midpoint theorem of the triangles,

"Segment joining midpoints of the two sides of a triangle is parallel to the third side and measure half the length of the third side."

Therefore, from the figure attached,

In ΔFGH,

J and K are the mid points of the two sides GH and FH.

By theorem, segment JK║GF and m(JK) =
`(1)/(2)m(FG)`

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

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

5y + 3 = 4y + 10

5y - 4y = 10 - 3

y = 7