Question

In MON, J, K, and L are midpoints. If JL = 11, LK = 13, and ON = 20, and JL || MN, LK || MO, and JK || ON, what is the length of MN, MO, and JK?

Answer 1

The lengths of MN is 22 units, MO is 26 units and JK is 10 units

Explanation:

A line segment joining the mid-points of two sides in a triangle is parallel to the third side and equal to half its length

In Δ MON

∵ J, K, and L are mid-points

∵ JL // MN and LK // MO

∴ L is the mid-point of ON

∴ J is the mid-point of MO

∴ K is the mid-point of MN

∵ J, L are the mid-points of MO and ON

∵ JL is opposite to MN

→ By using the rule above

∴ JL =
`(1)/(2)` MN

∵ JL = 11 units

∴ 11 =
`(1)/(2)` MN

→ Multiply both sides by 2

∴ 22 = MN

∴ MN = 22 units

∵ K, L are the mid-points of MN and ON

∵ KL is opposite to MO

→ By using the rule above

∴ KL =
`(1)/(2)` MO

∵ KL = 13 units

∴ 13 =
`(1)/(2)` MO

→ Multiply both sides by 2

∴ 26 = MO

∴ MO = 26 units

∵ J, K are the mid-points of MO and MN

∵ JK is opposite to ON

→ By using the rule above

∴ JK =
`(1)/(2)` ON

∵ ON =20 units

∴ JK =
`(1)/(2)` (20)

∴ JK = 10 units

∴ The lengths of MN are 22 units, MO is 26 units and JK is 10 units