Question

how to know its altitude
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Answer 1

construct the altitude in the angle made by the longest sides

Answer 2

Use heron's formula to find the area of the triangle and then equate it to the area of the triangle formula (1/2 × base × height).

Solution:

S (perimeter/2) = (35 + 54 + 61)/2 = 150/2 = 75cm

Using heron's formula to find the area,

Area = √(S(S-A)(S-B)(S-C))

        = √(75(75-35)(75-54)(75-61))

        = √(75(40)(21)(14))

        = √(75×11760)

        = √882000

        = 420√5 cm²

Now,

area = 1/2 × base × height

420√5 = 1/2 × 54 × height

420√5 = 27 × height

∴ height = (420√5)/27  =  (140√5)/9 cm