Question

guys anyone of u explain me 7 problem in a detailed manner

Answer 1

all three sides of a right angle triangle in AP .

let a , b , c are in AP which are sides of ∆

we know,
a/c to AP property ,
common difference always constant .

e.g b - a = c - b

a + c = 2b -------(1)

now ∆ is right angle ∆
so,

c^2 = a^2 + b^2

( c^2 - a^2) = b^2

( c - a)( c + a) = b^2

from equation (1)

2b( c - a) = b^2

c - a = b/2 -------(2)

solve equation(1) and (2)

2c = 5b/2

c = 5b/4

put c = 5b/4 in equation (1)
a = 2b -5b/4 = 3b/4

hence,
ratio of three sides ,
3b/4 : b : 5b/4
3 : 4 : 5

Answer 2

this is anther method , follow which is easy to u