The sides of a right angled triangle are in arithmetic progression. If the triangle has area 24, then what is the length of its smallest side?

Answer

6

Explanation

Let the sides be a-d,a,a+d such that `d gt 0 `
By Pthgoras theorem , we have
`a^2+(a-d)^2=(a+d)^2`
`rArr a = 4d`
Thus , sides are 3d ,4d and 5d
Given that area `=24= 1/2(3d)(4d)`
`rArr d = 2 `
Thus , sides are 6, 8 and 10 ,
Hence the smallest side is 6