Question

If the length of the sides of a triangle are in proportion 25 : 17 : 12 and its perimeter is 540 m, then find the lengths of the largest and smallest altitudes.

Answer 1

Answer:

$Largest \:side = 250\:m\\Smallest \:side = 120\:m$

Step-by-step explanation:

Given the length of the sides of a triangle are in proportion 25 : 17 : 12 and its perimeter is 540

$Let \: a,\:b, \:c \: are \: lengths \\of \: the \: sides \:of\:a\: triangle$

$a:b:c=25:17:12$

$Let\: a = 25x ,\\b= 17x,\\c=12x$

$Perimeter = 540\:m\:(given)$

$\implies a+b+c=540$

$\implies 25x+17x+12x=540$

$\implies 54x=540$

$\implies x = \frac{540}{54}\\=10$

$Now,\\a = 25x =25\times 10=250\:m ,\\b = 17x =17\times 10=170\:m \\c = 12x =12\times 10=120\:m$

Therefore,

$Largest \:side = 250\:m\\Smallest \:side = 120\:m$

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