Question

Geometry!
Use the diagram of triangle MNO where, X, Y, and Z are the midpoints of the sides.

Answer 1

YZ = 7 , MO = 8

Explanation:

A segment joining the midpoints of 2 sides of a triangle is half the length of the third side.

(11)

YZ =
`(1)/(2)` MN , that is

3x + 1 =
`(1)/(2)` (10x - 6) = 5x - 3 ( subtract 5x from both sides )

- 2x + 1 = - 3 ( subtract 1 from both sides )

- 2x = - 4 ( divide both sides by - 2 )

x = 2

Then

YZ = 3x + 1 = 3(2) + 1 = 6 + 1 = 7

(12)

XY =
`(1)/(2)` MO , that is

x - 1 =
`(1)/(2)` (3x - 7) ← multiply through by 2 to clear the fraction

2x - 2 = 3x - 7 ( subtract 3x from both sides )

- x - 2 = - 7 ( add 2 to both sides )

- x = - 5 ( multiply both sides by - 1 )

x = 5

Then

MO = 3x - 7 = 3(5) - 7 = 15 - 7 = 8