Question

solve this with prfect solution...

Answer 1

Let the sides of the triangle be a, b, c.

Let the respective altitudes on these sides be 10, 12 and 15.

Now the area of triangle (A) calculated using any side and the altitude over that side would be equal to,

1/2*a*10 =1/2*b*12 = 1/2*c*15 = A,

or,

a= 2A/10 = A/5

b= 2A/12 = A/6

c= 2A/15 = A/7.5

Semi-perimeter (s) would be,

s=(a+b+c)/2

= (2A/10+2A/12+2A/15)/2

=A/10+A/12+A/15

=A (1/10+1/12+1/15),

= A/4

and, s-a =(A/4)- (A/5) = A/20

s-b = (A/4)- (A/6) = A/12

s-c = (A/4)- (A/7.5) = 7A/60

Now, using Heron’s formula, area of triangle can be calculated as,

A = √[s*(s-a)(s-b)(s-c)]

So,

A= √[A/4]*[A/20]*[A/12]*[7A/60]

A = [(A*A)/240]* √[7]

A = 240/√7 = 90.7115

So,

semi-perimeter, s,

s=(a+b+c)/2

=A/4

= 90.7115/4

= 22.678


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