Question

if a b c are the sides of a triangle and s be its semiperimeter and (s-a)=90 (s-b)=50 (s-c)=10 then find value of a

Answer 1

Given, (s - a) = 90........(i)
(s - b) = 50 ........(ii)
(s - c) = 10 .........(iii)

adding all equations (i), (ii) and (iii),
(s - a) + (s - b) + (s - c) = 90 + 50 + 10

(s + s + s) - (a + b + c) = 150

3s - (a + b + c) = 150

we know, semiperimeter , s = (a + b + c)/2
so, (a + b + c) = 2s put it above ,

3s - 2s = 150

s = 150

now, from equation (1),

150 - a = 90
150 - 90 = a
a = 60

hence, value of a = 60