Question

If E and D are midpoints of ABC, find CB.
A. 3.1
B. 4.4
C. 5.2
D. 8.8

Answer 1

CB is 8.8 ⇒ D

Explanation:

In any triangle, the line segment joining the mid-points of two sides is parallel to the 3rd side and equal to half its length

In the given figure

∵ ABC is a triangle

∵ E and D are the midpoints of sides AC and AB

∵ CB is the 3rd side

→ By using the rule above

∴ ED // CB

∴ ED =
`(1)/(2)` CB

∵ ED = x + 0.7

∵ CB = 3x - 2.3

→ Substitute them in the equation above

∴ x + 0.7 =
`(1)/(2)` (3x - 2.3)

∴ x + 0.7 =
`(1)/(2)` (3x) -
`(1)/(2)` (2.3)

∴ x + 0.7 = 1.5x - 1.15

→ Subtract 1.5x from both sides

∵ x - 1.5x + 0.7 = 1.5x - 1.5x -1.15

∴ -0.5x + 0.7 = -1.15

→ Subtract 0.7 from both sides

∵ -0.5x + 0.7 - 0.7 = -1.15 - 0.7

∴ -0.5x = -1.85

→ Divide both sides by -0.5

∴ x = 3.7

→ Substitute x by 3.7 in the expression of CB

∵ CB = 3(3.7) - 2.3

∴ CB = 11.1 - 2.3

∴ CB = 8.8