Question

Find NMC triangle's perimeter if BO:BK=1:3 and ABC triangle's perimeter is 96

Answer 1

Answer:

  80

Step-by-step explanation:

If we assume the triangles are similar and are isosceles, and that BK is an altitude, then we can work the problem.

Triangle OKN will be similar to triangle BKA, so ...

  AN : AK = BO : BK = 1 : 3

Then ...

  AN : AK : KC = 1 : 3 : 3

In terms of ratio units, ...

  AN = 1

  AC = 3+3 = 6

  NC = 6-1 = 5

This means NC : AC = 5 : 6. The triangle perimeters will have the same ratio.

  perimeter(NMC) = 5/6·perimeter(ABC) = 5/6·96

  perimeter(NMC) = 80