Given: △abc, bk=10, ac=30, m∠nmo=90°, mn=mo, bk⊥ac, no∥ac, m∈ac find: no

12 unit.    

Step-by-step explanation:

Given : In triangle ABC,

m∠NMO=90°, MN=MO, BK⊥AC, NO∥AC, M∈AC,  BK=10, AC=30,

We have to find : NO

Since, NO∥AC,

By the alternative interior angle theorem,

Also,

Thus, by AAA similarity postulate,

Let S ∈ NO such that BS ⊥ NO,

By the property of similar triangles,

  -------- (1),

Now, m∠NMO=90° and MN=MO,

Let J ∈ NO, such that MJ⊥NO

⇒ Triangle NMO is a isosceles triangle,

⇒ ∠MNJ = 45°,

-------(2)

From equation (1),

Since, BK=10, AC=30

From equation (2),

NO = 2 × 6 = 12 unit.

9

step-by-step explanation:

so, converting firstly the mixed fractions to improper fractions and then "adding".