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The sides of a right angled triangle are...

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?

Text Solution

Verified by Experts

The correct Answer is:
6
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
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