The length of the longest altitude of the triangle is 24 √5 cm.
The sides of the triangle that are given are:
35 cm, 54 cm and 61 cm
We need to find the longest altitude of the triangle.
We know that:
s = ( a + b + c ) / 2
s = ( 35 + 54 + 61 ) / 2
s = 150 / 2
s = 75
s - a = 75 - 35
s - a = 40
s - b = 75 - 54
s - b = 21
s - c = 75 - 61
s - c = 14
Area, A = √ s (s − a)(s − b)(s − c)
A = √ 75 (40) (21) (14)
A = 420 √ 5 cm²
Now, area is also equal to:
Area = 1 / 2 × b × h
420 √5 = 1 / 2 × 35 × h
h = 420 √ 5 × 2 ÷ 35
h = 24 √5 cm
Therefore, the length of the longest altitude of the triangle is 24 √5 cm.
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